## Kuchment, Peter A.

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 Author ID: kuchment.peter-a Published as: Kuchment, Peter; Kuchment, P. A.; Kuchment, P.; Kuchment, Peter A. more...less Homepage: https://www.math.tamu.edu/~peter.kuchment/ External Links: MGP · ORCID · Google Scholar · Math-Net.Ru · dblp
 Documents Indexed: 141 Publications since 1972, including 4 Books 11 Contributions as Editor Reviewing Activity: 14 Reviews Co-Authors: 110 Co-Authors with 90 Joint Publications 3,613 Co-Co-Authors
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### Co-Authors

 53 single-authored 8 Kunyansky, Leonid A. 7 Semënov, Evgeniĭ Mikhaĭlovich 6 Agranovsky, Mark L. 5 Berkolaiko, Gregory 4 Sunada, Toshikazu 3 Braverman, Maxim 3 Do, Ngoc T. 3 Exner, Pavel 3 Friedlander, Leonid 3 Fulling, Stephen A. 3 Kreĭn, Selim Grigor’evich 3 Maz’ya, Vladimir Gilelevich 3 Novikov, Sergeĭ Petrovich 3 Ong, Beng-Seong 3 Quinto, Eric Todd 3 Terzioglu, Fatma 3 Vaĭnberg, Boris Rufimovich 2 Aguilar, Valentina 2 Ambartsoumian, Gaik 2 Bukhshtaber, Viktor Matveevich 2 Finch, David V. 2 Fridman, Buma L. 2 Gromov, Mikhael Leonidovich 2 Hristova, Yulia 2 Ivrii, Victor Ja. 2 Keating, Jonathan Peter 2 Kha, Minh 2 Kordyukov, Yuri A. 2 Lancaster, Kirk Eugene 2 Levendorskiĭ, Sergeĭ Zakharovich 2 Lin, Vladimir Ya. 2 L’Vin, Sergej Ya. 2 Lvin, Sergey J. 2 Pinchover, Yehuda 2 Raich, Andrew S. 2 Steinhauer, Dustin 2 Struppa, Daniele Carlo 2 Teplyaev, Alexander 2 Winn, Brian 2 Zaidenberg, Mikhail G. 1 Allmaras, Moritz 1 Auckly, David R. 1 Axmann, Waldemar 1 Baines, W. 1 Bal, Guillaume 1 Baras, John S. 1 Benchama, Noureddine 1 Berenstein, Carlos Alberto 1 Berezans’kyĭ, Yuriĭ Makarovych 1 Carroll, Raymond James 1 Chang, Der-Chen E. 1 Cheney, Margaret 1 Corbin, James E. 1 Darrow, David 1 Dikansky, Arnold 1 Egorov, Yuriĭ Vladimirovich 1 Ehrenpreis, Leon 1 Farkas, Hershel M. 1 Figotin, Alex 1 Figotin, Alexander 1 Freidlin, Mark I. 1 Gay, Roger 1 Gindikin, Simon Grigorevich 1 Harrison, Jon M. 1 Kanschat, Guido 1 Kappeler, Thomas 1 Kawai, Takahiro 1 Khovanskiĭ, Askold Georgievich 1 Komech, Alexander Ilich 1 Krasnenker, A. S. 1 Kutateladze, Semën Samsonovich 1 Lakshtanov, Evgeny L. 1 Li, Baoqin 1 Lissianoi, Serguei 1 Ma, Daowei 1 Mallick, Bani K. 1 McOwen, Robert C. 1 Mogilevskaya, Lyudmila 1 Mogilevsky, Mila 1 Molchanov, Stanislav Alekseevich 1 Napoletani, Domenico 1 Nguyen, Linh Anh 1 Novikov, Roman G. 1 Ovchinnikov, Vladimir I. 1 Papanicolaou, Vassilis G. 1 Post, Olaf 1 Ragusa, Jean C. 1 Reshetnyak, Yuriĭ Grigor’evich 1 Sabadini, Irene 1 Schotland, John C. 1 Sebbar, Ahmed 1 Shneiberg, Iosiph 1 Sklyadnev, S. A. 1 Smilansky, Uzy 1 Sobolev, Alexander V. 1 Sottile, Frank 1 Stefanov, Plamen D. 1 Sternberg, Shlomo 1 Taskinen, Jari 1 Taylor, Alan M. ...and 10 more Co-Authors
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### Serials

 11 Inverse Problems 8 Russian Mathematical Surveys 7 Soviet Mathematics. Doklady 6 Contemporary Mathematics 5 Functional Analysis and its Applications 4 Journal of Physics A: Mathematical and Theoretical 4 Inverse Problems and Imaging 3 Uspekhi Matematicheskikh Nauk [N. S.] 3 Waves in Random Media 3 Akademiya Nauk Moldavskoĭ SSR. Ordena Trudovogo Krasnogo Znameni Institut Matematiki s Vychislitel’nym Tsentrom. Matematicheskie Issledovaniya 3 SIAM Journal on Applied Mathematics 3 Notices of the American Mathematical Society 2 Applicable Analysis 2 Communications in Mathematical Physics 2 Journal of Mathematical Physics 2 Journal of Functional Analysis 2 Matematicheskiĭ Sbornik. Novaya Seriya 2 Mathematics of the USSR. Izvestiya 2 Transactions of the American Mathematical Society 2 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 2 Mathematics of the USSR, Sbornik 2 Bulletin of the American Mathematical Society. New Series 2 Journal of Spectral Theory 1 American Mathematical Monthly 1 Journal d’Analyse Mathématique 1 Journal of Computational Physics 1 Journal of Mathematical Analysis and Applications 1 Journal of Statistical Physics 1 Differentsial’nye Uravneniya 1 Funktsional’nyĭ Analiz i ego Prilozheniya 1 Journal of Differential Equations 1 Kibernetika 1 Mathematische Nachrichten 1 Acta Applicandae Mathematicae 1 European Journal of Applied Mathematics 1 The Journal of Geometric Analysis 1 Geometric and Functional Analysis. GAFA 1 Communications in Partial Differential Equations 1 Journal of Physics A: Mathematical and General 1 SIAM Journal on Mathematical Analysis 1 Experimental Mathematics 1 Memoirs on Differential Equations and Mathematical Physics 1 Advances in Computational Mathematics 1 CBMS-NSF Regional Conference Series in Applied Mathematics 1 Lecture Notes in Mathematics 1 Mathematical Surveys and Monographs 1 Proceedings of Symposia in Pure Mathematics 1 Complex Analysis and Operator Theory 1 SIAM Journal on Imaging Sciences 1 Optimizacija 1 Analysis and Mathematical Physics 1 Nanoscale Systems: Mathematical Modeling, Theory and Applications 1 Pure and Applied Functional Analysis 1 Operator Theory: Advances and Applications 1 Translations. Series 2. American Mathematical Society
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### Fields

 76 Partial differential equations (35-XX) 29 Operator theory (47-XX) 29 Biology and other natural sciences (92-XX) 28 Quantum theory (81-XX) 25 Integral transforms, operational calculus (44-XX) 24 Global analysis, analysis on manifolds (58-XX) 21 Numerical analysis (65-XX) 20 Optics, electromagnetic theory (78-XX) 16 History and biography (01-XX) 12 General and overarching topics; collections (00-XX) 10 Statistical mechanics, structure of matter (82-XX) 9 Ordinary differential equations (34-XX) 8 Combinatorics (05-XX) 7 Functional analysis (46-XX) 6 Several complex variables and analytic spaces (32-XX) 6 Algebraic topology (55-XX) 5 Abstract harmonic analysis (43-XX) 5 Differential geometry (53-XX) 5 Manifolds and cell complexes (57-XX) 4 Mechanics of deformable solids (74-XX) 4 Information and communication theory, circuits (94-XX) 3 Functions of a complex variable (30-XX) 3 Approximations and expansions (41-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Computer science (68-XX) 3 Fluid mechanics (76-XX) 2 Topological groups, Lie groups (22-XX) 2 Difference and functional equations (39-XX) 2 Geometry (51-XX) 2 General topology (54-XX) 2 Operations research, mathematical programming (90-XX) 1 Algebraic geometry (14-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Special functions (33-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral equations (45-XX) 1 Convex and discrete geometry (52-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX)

### Citations contained in zbMATH Open

103 Publications have been cited 2,457 times in 1,350 Documents Cited by Year
Introduction to quantum graphs. Zbl 1318.81005
Berkolaiko, Gregory; Kuchment, Peter
2013
Floquet theory for partial differential equations. Zbl 0789.35002
Kuchment, Peter
1993
Quantum graphs. I: Some basic structures. Zbl 1063.81058
Kuchment, Peter
2004
Quantum graphs. II: Some spectral properties of quantum and combinatorial graphs. Zbl 1070.81062
Kuchment, Peter
2005
Mathematics of thermoacoustic tomography. Zbl 1185.35327
Kuchment, Peter; Kunyansky, Leonid
2008
Graph models for waves in thin structures. Zbl 1063.35525
Kuchment, Peter
2002
On the spectra of carbon nano-structures. Zbl 1145.81032
Kuchment, Peter; Post, Olaf
2007
An overview of periodic elliptic operators. Zbl 1346.35170
Kuchment, Peter
2016
The mathematics of photonic crystals. Zbl 0986.78004
Kuchment, Peter
2001
Reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media. Zbl 1180.35563
Hristova, Yulia; Kuchment, Peter; Nguyen, Linh
2008
Band-gap structure of spectra of periodic dielectric and acoustic media. I: Scalar model. Zbl 0852.35014
Figotin, Alex; Kuchment, Peter
1996
Floquet theory for partial differential equations. Zbl 0519.35003
Kuchment, P. A.
1982
Quantum graphs and their applications. Proceedings of an AMS-IMS-SIAM joint summer research conference on quantum graphs and their applications, Snowbird, UT, USA, June 19–23, 2005. Zbl 1098.81007
2006
The Radon transform and medical imaging. Zbl 1282.92001
Kuchment, Peter
2014
Analysis on graphs and its applications. Selected papers based on the Isaac Newton Institute for Mathematical Sciences programme, Cambridge, UK, January 8–June 29, 2007. Zbl 1143.05002
2008
Band-gap structure of spectra of periodic dielectric and acoustic media. II: Two-dimensional photonic crystals. Zbl 0868.35009
Figotin, A.; Kuchment, P.
1996
Quantum graphs: an introduction and a brief survey. Zbl 1210.05169
Kuchment, Peter
2008
An efficient finite element method for computing spectra of photonic and acoustic band-gap materials. I: Scalar case. Zbl 0963.78028
Axmann, Waldemar; Kuchment, Peter
1999
Convergence of spectra of mesoscopic systems collapsing onto a graph. Zbl 0982.35076
Kuchment, Peter; Zeng, Hongbiao
2001
Dependence of the spectrum of a quantum graph on vertex conditions and edge lengths. Zbl 1317.81127
Berkolaiko, G.; Kuchment, P.
2012
Mathematics of photoacoustic and thermoacoustic tomography. Zbl 1259.92065
Kuchment, Peter; Kunyansky, Leonid
2011
Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography with variable sound speed. Zbl 1126.35087
Agranovsky, Mark; Kuchment, Peter
2007
Spectral properties of classical waves in high-contrast periodic media. Zbl 0916.35011
Figotin, A.; Kuchment, P.
1998
Stabilizing inverse problems by internal data. Zbl 1252.92037
Kuchment, Peter; Steinhauer, Dustin
2012
Approximation by spherical waves in $$L^p$$-spaces. Zbl 0898.44003
Agranovsky, Mark; Berenstein, Carlos; Kuchment, Peter
1996
Banach bundles and linear operators. Zbl 0335.47017
Zaĭdenberg, M. G.; Kreĭn, S. G.; Kuchment, P. A.; Pankov, A. A.
1975
Index theorems for quantum graphs. Zbl 1127.58027
Fulling, S. A.; Kuchment, P.; Wilson, J. H.
2007
Range descriptions for the spherical mean Radon transform. Zbl 1132.44002
Agranovsky, Mark; Kuchment, Peter; Quinto, Eric Todd
2007
On local tomography. Zbl 0832.44001
Kuchment, Peter; Lancaster, Kirk; Mogilevskaya, Lyudmila
1995
On occurrence of spectral edges for periodic operators inside the Brillouin zone. Zbl 1141.82340
Harrison, Jon M.; Kuchment, P.; Sobolev, A.; Winn, B.
2007
Asymptotics of spectra of Neumann Laplacians in thin domains. Zbl 1050.35094
Kuchment, Peter; Zeng, Honbiao
2003
A range description for the planar circular Radon transform. Zbl 1120.44003
Ambartsoumian, Gaik; Kuchment, Peter
2007
On the structure of spectra of periodic elliptic operators. Zbl 1058.35174
Kuchment, Peter; Levendorskiĭ, Sergei
2002
On the injectivity of the circular Radon transform. Zbl 1072.44001
Ambartsoumian, Gaik; Kuchment, Peter
2005
On absence of embedded eigenvalues for Schrödinger operators with perturbed periodic potentials. Zbl 0960.35077
Kuchment, Peter; Vainberg, Boris
2000
Quantum graph spectra of a graphyne structure. Zbl 1273.81067
Do, Ngoc T.; Kuchment, Peter
2013
Mathematics of hybrid imaging: A brief review. Zbl 1248.65102
Kuchment, Peter
2012
On the structure of eigenfunctions corresponding to embedded eigenvalues of locally perturbed periodic graph operators. Zbl 1125.39021
Kuchment, Peter; Vainberg, Boris
2006
Spectral properties of high contrast band-gap materials and operators on graphs. Zbl 0930.35112
Kuchment, Peter; Kunyansky, Leonid A.
1999
Banach bundles and linear operators. Zbl 0317.47018
Zaĭdenberg, M. G.; Kreĭn, S. G.; Kuchment, P. A.; Pankov, A. A.
1975
Detecting small low emission radiating sources. Zbl 1266.82083
Allmaras, Moritz; Darrow, David; Hristova, Yulia; Kanschat, Guido; Kuchment, Peter
2013
Integral representations and Liouville theorems for solutions of periodic elliptic equations. Zbl 0986.35028
Kuchment, Peter; Pinchover, Yehuda
2001
On the location of spectral edges in $$\mathbb Z$$-periodic media. Zbl 1204.81063
Exner, Pavel; Kuchment, Peter; Winn, Brian
2010
Compton camera imaging and the cone transform: a brief overview. Zbl 1478.68410
Terzioglu, Fatma; Kuchment, Peter; Kunyansky, Leonid
2018
Mathematics of photoacoustic and thermoacoustic tomography. 2nd edition. Zbl 1331.92076
Kuchment, Peter; Kunyansky, Leonid
2015
Three-dimensional image reconstruction from Compton camera data. Zbl 1354.44002
Kuchment, Peter; Terzioglu, Fatma
2016
2D and 3D reconstructions in acousto-electric tomography. Zbl 1217.35211
Kuchment, Peter; Kunyansky, Leonid
2011
Differential operators on graphs and photonic crystals. Zbl 0993.65122
Kuchment, P.; Kunyansky, L.
2002
Liouville theorems and spectral edge behavior on Abelian coverings of compact manifolds. Zbl 1127.58015
Kuchment, Peter; Pinchover, Yehuda
2007
Tight frames of exponentially decaying Wannier functions. Zbl 1154.82028
Kuchment, Peter
2009
Reconstruction of a continuous representation with respect to a subrepresentation and a factor representation. Zbl 0332.46047
Kuchment, P. A.
1976
Range conditions for a spherical mean transform. Zbl 1190.44001
Agranovsky, Mark; Finch, David; Kuchment, Peter
2009
Inversion of weighted divergent beam and cone transforms. Zbl 1372.44004
Kuchment, Peter; Terzioglu, Fatma
2017
Critical partitions and nodal deficiency of billiard eigenfunctions. Zbl 1308.35152
Berkolaiko, Gregory; Kuchment, Peter; Smilansky, Uzy
2012
One some spectral problems of mathematical physics. Zbl 1061.35065
Kuchment, Peter
2004
Generalized transforms of Radon type and their applications. Zbl 1118.44001
Kuchment, Peter
2006
Stabilizing inverse problems by internal data. II: Non-local internal data and generic linearized uniqueness. Zbl 1330.35427
Kuchment, Peter; Steinhauer, Dustin
2015
Synthetic focusing in ultrasound modulated tomography. Zbl 1286.44002
Kuchment, Peter; Kunyansky, Leonid
2010
Some inversion formulas in the single photon emission computed tomography. Zbl 0839.44002
Kuchment, Peter; Shneiberg, Iosiph
1994
On the Floquet theory of periodic difference equations. Zbl 0979.39011
Kuchment, P. A.
1991
On guided waves in photonic crystal waveguides. Zbl 1046.35081
Kuchment, Peter; Ong, BengSeong
2003
Green’s function asymptotics near the internal edges of spectra of periodic elliptic operators: Spectral edge case. Zbl 1257.35080
Kuchment, Peter; Raich, Andrew
2012
A Bayesian approach to the detection of small low emission sources. Zbl 1228.62035
Xun, Xiaolei; Mallick, Bani; Carroll, Raymond J.; Kuchment, Peter
2011
Range conditions for the exponential Radon transform. Zbl 0858.44002
Aguilar, Valentina; Ehrenpreis, Leon; Kuchment, Peter
1996
Vladimir A. Geyler, April 29, 1943–April 2, 2007. Zbl 1190.01017
Exner, Pavel; Keating, Jonathan P.; Kuchment, Peter; Sunada, Toshikazu; Teplyaev, Alexander
2008
Differential and pseudo-differential operators on graphs as models of mesoscopic systems. Zbl 1200.82086
Kuchment, Peter
2003
Green’s function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral gap interior. Zbl 1394.35297
Kha, Minh; Kuchment, Peter; Raich, Andrew
2017
On guided electromagnetic waves in photonic crystal waveguides. Zbl 1217.35181
Kuchment, Peter; Ong, Beng-Seong
2010
On embedding eigenvalues of perturbed periodic Schrödinger operators. Zbl 0902.35077
Kuchment, Peter; Vainberg, Boris
1998
Band-gap structure of the spectrum of periodic Maxwell operators. Zbl 0946.82517
Figotin, Alexander; Kuchment, Peter
1994
Paley-Wiener theorem for exponential Radon transform. Zbl 0705.44001
Kuchment, Peter A.; L’Vin, Sergej Ya.
1990
On the question of the affine-invariant points of convex bodies. Zbl 0263.52004
Kuchment, P. A.
1972
Numerical harmonic analysis on the hyperbolic plane. Zbl 1022.65145
Fridman, Buma; Kuchment, Peter; Lancaster, Kirk; Lissianoi, Serguei; Mogilevsky, Mila
2000
Range conditions for the multidimensional exponential x-ray transform. Zbl 0843.44005
Aguilar, Valentina; Kuchment, Peter
1995
Solution of the linearized inverse conductivity problem in a half space via integral geometry. Zbl 0904.35096
Fridman, Buma; Kuchment, Peter; Ma, Daowei; Papanicolaou, Vassilis G.
1998
Analyticity of the spectrum and Dirichlet-to-Neumann operator technique for quantum graphs. Zbl 1422.81110
Kuchment, Peter; Zhao, Jia
2019
On inversion and range characterization of one transform arising in emission tomography. Zbl 0823.44007
Kuchment, P.
1994
On the behavior of Floquet exponents of a kind of periodic evolution problems. Zbl 0792.35026
Kuchment, Peter
1994
Iosif Shneiberg, July 26, 1950 - July 21, 1992. Zbl 0938.01043
Krein, Selim; Kuchment, Peter; Ovchinnikov, Vladimir; Semenov, Evgeny
1999
2D photonic crystals with cubic structure: Asymptotic analysis. Zbl 0901.65078
Figotin, A.; Kuchment, P.
1998
The range of the exponential Radon transform. Zbl 0748.44002
Kuchment, P. A.; L’vin, S. Ya.
1990
Floquet representation of solutions of linear hypoelliptic systems of partial differential equations. Zbl 0414.35020
Kuchment, P. A.
1979
Generic properties of dispersion relations for discrete periodic operators. Zbl 1454.81060
Do, Ngoc; Kuchment, Peter; Sottile, Frank
2020
The support theorem for the single radius spherical mean transform. Zbl 1254.44001
Agranovsky, M.; Kuchment, P.
2011
On Parseval frames of exponentially decaying composite Wannier functions. Zbl 1428.35417
Auckly, David; Kuchment, Peter
2018
Spherical representation of solutions of invariant differential equations on a symmetric Riemannian space of noncompact type. Zbl 0593.58044
Kuchment, P. A.
1985
Bloch solutions of periodic partial differential equations. Zbl 0459.35028
Kuchment, P. A.
1980
The absence of $$L_ 2-$$solutions for periodic partial differential equations. Zbl 0461.35029
Kuchment, P. A.
1980
Representations of solutions of invariant differential equations on certain symmetric spaces. Zbl 0497.58025
Kuchment, P. A.
1981
On absolute continuity of spectra of periodic elliptic operators. Zbl 0965.35100
Kuchment, Peter; Levendorskiǐ, Sergei
1999
On positivity problems for the Radon transform and some related transforms. Zbl 0785.44003
Kuchment, Peter
1992
Tomography, impedance imaging, and integral geometry. 1993 AMS-SIAM summer seminar, June 7-18, 1993, Mount Holyoke College, South Hadley, MA,, USA. Zbl 0801.00052
1994
Integral representations of solutions of periodic elliptic equations. Zbl 1133.35033
Kuchment, Peter
2007
Voronezh winter mathematical schools. Dedicated to Selim Krein. Zbl 0997.00561
1998
A remark on the homotopy type of the group of $$J$$-unitary operators. Zbl 0355.47027
Kuchment, P. A.
1974
On the Floquet representation of exponentially increasing solutions of elliptic equations with periodic coefficients. Zbl 0393.35009
Zelenko, L. B.; Kuchment, P. A.
1978
On classifying spaces for the groups $$K^{p,q}_G(X)$$. Zbl 0268.55002
Kuchment, P. A.; Pankov, A. A.
1972
Special issue: Dedicated to Professor Robert Brooks. Zbl 1076.81500
2004
Coincidence of length spectra does not imply isospectrality. Zbl 1083.35077
Fulling, S. A.; Kuchment, Peter
2005
Remembering Leon Ehrenpreis (1930–2010). Zbl 1225.01086
Struppa, Daniele C.; Farkas, Hershel; Kawai, Takahiro; Kuchment, Peter; Quinto, Eric Todd; Sternberg, Shlomo; Taylor, Alan
2011
Generic properties of dispersion relations for discrete periodic operators. Zbl 1454.81060
Do, Ngoc; Kuchment, Peter; Sottile, Frank
2020
Analyticity of the spectrum and Dirichlet-to-Neumann operator technique for quantum graphs. Zbl 1422.81110
Kuchment, Peter; Zhao, Jia
2019
Compton camera imaging and the cone transform: a brief overview. Zbl 1478.68410
Terzioglu, Fatma; Kuchment, Peter; Kunyansky, Leonid
2018
On Parseval frames of exponentially decaying composite Wannier functions. Zbl 1428.35417
Auckly, David; Kuchment, Peter
2018
Inversion of weighted divergent beam and cone transforms. Zbl 1372.44004
Kuchment, Peter; Terzioglu, Fatma
2017
Green’s function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral gap interior. Zbl 1394.35297
Kha, Minh; Kuchment, Peter; Raich, Andrew
2017
An overview of periodic elliptic operators. Zbl 1346.35170
Kuchment, Peter
2016
Three-dimensional image reconstruction from Compton camera data. Zbl 1354.44002
Kuchment, Peter; Terzioglu, Fatma
2016
Mathematics of photoacoustic and thermoacoustic tomography. 2nd edition. Zbl 1331.92076
Kuchment, Peter; Kunyansky, Leonid
2015
Stabilizing inverse problems by internal data. II: Non-local internal data and generic linearized uniqueness. Zbl 1330.35427
Kuchment, Peter; Steinhauer, Dustin
2015
The Radon transform and medical imaging. Zbl 1282.92001
Kuchment, Peter
2014
Introduction to quantum graphs. Zbl 1318.81005
Berkolaiko, Gregory; Kuchment, Peter
2013
Quantum graph spectra of a graphyne structure. Zbl 1273.81067
Do, Ngoc T.; Kuchment, Peter
2013
Detecting small low emission radiating sources. Zbl 1266.82083
Allmaras, Moritz; Darrow, David; Hristova, Yulia; Kanschat, Guido; Kuchment, Peter
2013
Identities for $$\sin x$$ that came from medical imaging. Zbl 1278.33001
Kuchment, Peter; Lvin, Sergey
2013
Dependence of the spectrum of a quantum graph on vertex conditions and edge lengths. Zbl 1317.81127
Berkolaiko, G.; Kuchment, P.
2012
Stabilizing inverse problems by internal data. Zbl 1252.92037
Kuchment, Peter; Steinhauer, Dustin
2012
Mathematics of hybrid imaging: A brief review. Zbl 1248.65102
Kuchment, Peter
2012
Critical partitions and nodal deficiency of billiard eigenfunctions. Zbl 1308.35152
Berkolaiko, Gregory; Kuchment, Peter; Smilansky, Uzy
2012
Green’s function asymptotics near the internal edges of spectra of periodic elliptic operators: Spectral edge case. Zbl 1257.35080
Kuchment, Peter; Raich, Andrew
2012
Mathematics of photoacoustic and thermoacoustic tomography. Zbl 1259.92065
Kuchment, Peter; Kunyansky, Leonid
2011
2D and 3D reconstructions in acousto-electric tomography. Zbl 1217.35211
Kuchment, Peter; Kunyansky, Leonid
2011
A Bayesian approach to the detection of small low emission sources. Zbl 1228.62035
Xun, Xiaolei; Mallick, Bani; Carroll, Raymond J.; Kuchment, Peter
2011
The support theorem for the single radius spherical mean transform. Zbl 1254.44001
Agranovsky, M.; Kuchment, P.
2011
Remembering Leon Ehrenpreis (1930–2010). Zbl 1225.01086
Struppa, Daniele C.; Farkas, Hershel; Kawai, Takahiro; Kuchment, Peter; Quinto, Eric Todd; Sternberg, Shlomo; Taylor, Alan
2011
Spectral theory and geometric analysis. International conference in honor of Mikhail Shubin’s 65th birthday, Northeastern University, Boston, MA, USA, July 29 – August 2, 2009. Zbl 1207.58001
2011
On the location of spectral edges in $$\mathbb Z$$-periodic media. Zbl 1204.81063
Exner, Pavel; Kuchment, Peter; Winn, Brian
2010
Synthetic focusing in ultrasound modulated tomography. Zbl 1286.44002
Kuchment, Peter; Kunyansky, Leonid
2010
On guided electromagnetic waves in photonic crystal waveguides. Zbl 1217.35181
Kuchment, Peter; Ong, Beng-Seong
2010
Tight frames of exponentially decaying Wannier functions. Zbl 1154.82028
Kuchment, Peter
2009
Range conditions for a spherical mean transform. Zbl 1190.44001
Agranovsky, Mark; Finch, David; Kuchment, Peter
2009
Mathematics of thermoacoustic tomography. Zbl 1185.35327
Kuchment, Peter; Kunyansky, Leonid
2008
Reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media. Zbl 1180.35563
Hristova, Yulia; Kuchment, Peter; Nguyen, Linh
2008
Analysis on graphs and its applications. Selected papers based on the Isaac Newton Institute for Mathematical Sciences programme, Cambridge, UK, January 8–June 29, 2007. Zbl 1143.05002
2008
Quantum graphs: an introduction and a brief survey. Zbl 1210.05169
Kuchment, Peter
2008
Vladimir A. Geyler, April 29, 1943–April 2, 2007. Zbl 1190.01017
Exner, Pavel; Keating, Jonathan P.; Kuchment, Peter; Sunada, Toshikazu; Teplyaev, Alexander
2008
On the spectra of carbon nano-structures. Zbl 1145.81032
Kuchment, Peter; Post, Olaf
2007
Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography with variable sound speed. Zbl 1126.35087
Agranovsky, Mark; Kuchment, Peter
2007
Index theorems for quantum graphs. Zbl 1127.58027
Fulling, S. A.; Kuchment, P.; Wilson, J. H.
2007
Range descriptions for the spherical mean Radon transform. Zbl 1132.44002
Agranovsky, Mark; Kuchment, Peter; Quinto, Eric Todd
2007
On occurrence of spectral edges for periodic operators inside the Brillouin zone. Zbl 1141.82340
Harrison, Jon M.; Kuchment, P.; Sobolev, A.; Winn, B.
2007
A range description for the planar circular Radon transform. Zbl 1120.44003
Ambartsoumian, Gaik; Kuchment, Peter
2007
Liouville theorems and spectral edge behavior on Abelian coverings of compact manifolds. Zbl 1127.58015
Kuchment, Peter; Pinchover, Yehuda
2007
Integral representations of solutions of periodic elliptic equations. Zbl 1133.35033
Kuchment, Peter
2007
Quantum graphs and their applications. Proceedings of an AMS-IMS-SIAM joint summer research conference on quantum graphs and their applications, Snowbird, UT, USA, June 19–23, 2005. Zbl 1098.81007
2006
On the structure of eigenfunctions corresponding to embedded eigenvalues of locally perturbed periodic graph operators. Zbl 1125.39021
Kuchment, Peter; Vainberg, Boris
2006
Generalized transforms of Radon type and their applications. Zbl 1118.44001
Kuchment, Peter
2006
Quantum graphs. II: Some spectral properties of quantum and combinatorial graphs. Zbl 1070.81062
Kuchment, Peter
2005
On the injectivity of the circular Radon transform. Zbl 1072.44001
Ambartsoumian, Gaik; Kuchment, Peter
2005
Coincidence of length spectra does not imply isospectrality. Zbl 1083.35077
Fulling, S. A.; Kuchment, Peter
2005
Quantum graphs. I: Some basic structures. Zbl 1063.81058
Kuchment, Peter
2004
One some spectral problems of mathematical physics. Zbl 1061.35065
Kuchment, Peter
2004
Special issue: Dedicated to Professor Robert Brooks. Zbl 1076.81500
2004
Asymptotics of spectra of Neumann Laplacians in thin domains. Zbl 1050.35094
Kuchment, Peter; Zeng, Honbiao
2003
On guided waves in photonic crystal waveguides. Zbl 1046.35081
Kuchment, Peter; Ong, BengSeong
2003
Differential and pseudo-differential operators on graphs as models of mesoscopic systems. Zbl 1200.82086
Kuchment, Peter
2003
Waves in periodic and random media. Proceedings of an AMS-IMS-SIAM joint summer research conference, South Hadley, MA, USA, June 22–28, 2002. Zbl 1029.00026
2003
Graph models for waves in thin structures. Zbl 1063.35525
Kuchment, Peter
2002
On the structure of spectra of periodic elliptic operators. Zbl 1058.35174
Kuchment, Peter; Levendorskiĭ, Sergei
2002
Differential operators on graphs and photonic crystals. Zbl 0993.65122
Kuchment, P.; Kunyansky, L.
2002
The mathematics of photonic crystals. Zbl 0986.78004
Kuchment, Peter
2001
Convergence of spectra of mesoscopic systems collapsing onto a graph. Zbl 0982.35076
Kuchment, Peter; Zeng, Hongbiao
2001
Integral representations and Liouville theorems for solutions of periodic elliptic equations. Zbl 0986.35028
Kuchment, Peter; Pinchover, Yehuda
2001
On absence of embedded eigenvalues for Schrödinger operators with perturbed periodic potentials. Zbl 0960.35077
Kuchment, Peter; Vainberg, Boris
2000
Numerical harmonic analysis on the hyperbolic plane. Zbl 1022.65145
Fridman, Buma; Kuchment, Peter; Lancaster, Kirk; Lissianoi, Serguei; Mogilevsky, Mila
2000
An efficient finite element method for computing spectra of photonic and acoustic band-gap materials. I: Scalar case. Zbl 0963.78028
Axmann, Waldemar; Kuchment, Peter
1999
Spectral properties of high contrast band-gap materials and operators on graphs. Zbl 0930.35112
Kuchment, Peter; Kunyansky, Leonid A.
1999
Iosif Shneiberg, July 26, 1950 - July 21, 1992. Zbl 0938.01043
Krein, Selim; Kuchment, Peter; Ovchinnikov, Vladimir; Semenov, Evgeny
1999
On absolute continuity of spectra of periodic elliptic operators. Zbl 0965.35100
Kuchment, Peter; Levendorskiǐ, Sergei
1999
Spectral properties of classical waves in high-contrast periodic media. Zbl 0916.35011
Figotin, A.; Kuchment, P.
1998
On embedding eigenvalues of perturbed periodic Schrödinger operators. Zbl 0902.35077
Kuchment, Peter; Vainberg, Boris
1998
Solution of the linearized inverse conductivity problem in a half space via integral geometry. Zbl 0904.35096
Fridman, Buma; Kuchment, Peter; Ma, Daowei; Papanicolaou, Vassilis G.
1998
2D photonic crystals with cubic structure: Asymptotic analysis. Zbl 0901.65078
Figotin, A.; Kuchment, P.
1998
Voronezh winter mathematical schools. Dedicated to Selim Krein. Zbl 0997.00561
1998
Band-gap structure of spectra of periodic dielectric and acoustic media. I: Scalar model. Zbl 0852.35014
Figotin, Alex; Kuchment, Peter
1996
Band-gap structure of spectra of periodic dielectric and acoustic media. II: Two-dimensional photonic crystals. Zbl 0868.35009
Figotin, A.; Kuchment, P.
1996
Approximation by spherical waves in $$L^p$$-spaces. Zbl 0898.44003
Agranovsky, Mark; Berenstein, Carlos; Kuchment, Peter
1996
Range conditions for the exponential Radon transform. Zbl 0858.44002
Aguilar, Valentina; Ehrenpreis, Leon; Kuchment, Peter
1996
On local tomography. Zbl 0832.44001
Kuchment, Peter; Lancaster, Kirk; Mogilevskaya, Lyudmila
1995
Range conditions for the multidimensional exponential x-ray transform. Zbl 0843.44005
Aguilar, Valentina; Kuchment, Peter
1995
Some inversion formulas in the single photon emission computed tomography. Zbl 0839.44002
Kuchment, Peter; Shneiberg, Iosiph
1994
Band-gap structure of the spectrum of periodic Maxwell operators. Zbl 0946.82517
Figotin, Alexander; Kuchment, Peter
1994
On inversion and range characterization of one transform arising in emission tomography. Zbl 0823.44007
Kuchment, P.
1994
On the behavior of Floquet exponents of a kind of periodic evolution problems. Zbl 0792.35026
Kuchment, Peter
1994
Tomography, impedance imaging, and integral geometry. 1993 AMS-SIAM summer seminar, June 7-18, 1993, Mount Holyoke College, South Hadley, MA,, USA. Zbl 0801.00052
1994
Floquet theory for partial differential equations. Zbl 0789.35002
Kuchment, Peter
1993
On positivity problems for the Radon transform and some related transforms. Zbl 0785.44003
Kuchment, Peter
1992
On the Floquet theory of periodic difference equations. Zbl 0979.39011
Kuchment, P. A.
1991
Paley-Wiener theorem for exponential Radon transform. Zbl 0705.44001
Kuchment, Peter A.; L&rsquo;Vin, Sergej Ya.
1990
The range of the exponential Radon transform. Zbl 0748.44002
Kuchment, P. A.; L&rsquo;vin, S. Ya.
1990
Spherical representation of solutions of invariant differential equations on a symmetric Riemannian space of noncompact type. Zbl 0593.58044
Kuchment, P. A.
1985
Floquet theory for partial differential equations. Zbl 0519.35003
Kuchment, P. A.
1982
Representations of solutions of invariant differential equations on certain symmetric spaces. Zbl 0497.58025
Kuchment, P. A.
1981
Bloch solutions of periodic partial differential equations. Zbl 0459.35028
Kuchment, P. A.
1980
The absence of $$L_ 2-$$solutions for periodic partial differential equations. Zbl 0461.35029
Kuchment, P. A.
1980
Floquet representation of solutions of linear hypoelliptic systems of partial differential equations. Zbl 0414.35020
Kuchment, P. A.
1979
On the Floquet representation of exponentially increasing solutions of elliptic equations with periodic coefficients. Zbl 0393.35009
Zelenko, L. B.; Kuchment, P. A.
1978
Reconstruction of a continuous representation with respect to a subrepresentation and a factor representation. Zbl 0332.46047
Kuchment, P. A.
1976
Banach bundles and linear operators. Zbl 0335.47017
Zaĭdenberg, M. G.; Kreĭn, S. G.; Kuchment, P. A.; Pankov, A. A.
1975
Banach bundles and linear operators. Zbl 0317.47018
Zaĭdenberg, M. G.; Kreĭn, S. G.; Kuchment, P. A.; Pankov, A. A.
1975
...and 3 more Documents
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### Cited by 1,428 Authors

 53 Nazarov, Sergeĭ Aleksandrovich 37 Exner, Pavel 31 Kuchment, Peter A. 25 Haltmeier, Markus 21 Kurasov, Pavel B. 20 Pankrashkin, Konstantin 19 Moon, Sunghwan 17 Berkolaiko, Gregory 17 Scherzer, Otmar 16 Yang, Chuanfu 15 Ammari, Habib M. 14 Bondarenko, Natalia P. 13 Band, Ram 13 Mugnolo, Delio 13 Post, Olaf 13 Rabinovich, Vladimir Samuilovich 13 Weinstein, Michael I. 12 Bal, Guillaume 12 De Nittis, Giuseppe 12 Quinto, Eric Todd 11 Adami, Riccardo 11 Taskinen, Jari 10 Alberti, Giovanni S. 10 Borisov, Denis Ivanovich 10 Cacciapuoti, Claudio 10 Dovetta, Simone 10 Lotoreichik, Vladimir 10 Pelinovsky, Dmitry Efimovich 10 Rohleder, Jonathan 9 Bakharev, Fedor L’vovich 9 Kunyansky, Leonid A. 9 Lenz, Daniel H. 9 Niikuni, Hiroaki 9 Noja, Diego 9 Popov, Igor’ Yur’evich 9 Rubin, Boris 8 Ambartsoumian, Gaik 8 Cherednichenko, Kirill D. 8 Danilov, Leonid Ivanovich 8 Joly, Patrick 8 Shipman, Stephen P. 8 Teplyaev, Alexander 8 Uhlmann, Gunther Alberto 8 Veselić, Ivan 7 Cardone, Giuseppe 7 Khrabustovskyi, Andrii 7 Korotyaev, Evgeny L. 7 Roy, Souvik 7 Saburova, Natalia 7 Serra, Enrico 7 Tentarelli, Lorenzo 7 Vaĭnberg, Boris Rufimovich 7 Weder, Ricardo A. 6 Agranovsky, Mark L. 6 Behrndt, Jussi 6 Cornean, Horia D. 6 Goloshchapova, Nataliia 6 Kennedy, James Bernard 6 Klopp, Frédéric 6 Leugering, Günter 6 Lipovský, Jiří 6 Malamud, Mark M. 6 Monaco, Domenico 6 Ren, Kui 6 Seifert, Christian 6 Tamasan, Alexandru 6 Tilli, Paolo 6 Turek, Ondřej 6 Zhang, Chuanzeng 6 Zheng, Hui 5 Albeverio, Sergio A. 5 Angulo Pava, Jaime 5 Banasiak, Jacek 5 Bergounioux, Maïtine 5 Blinova, Irina V. 5 Bolte, Jens 5 Chernyshev, Vsevolod L. 5 Dong, Yiqiu 5 Engström, Christian 5 Fefferman, Charles Louis 5 Figotin, Alexander 5 Fillman, Jake 5 Finco, Domenico 5 Fliss, Sonia 5 Frikel, Jürgen 5 Giani, Stefano 5 Gomi, Kiyonori 5 Helffer, Bernard 5 Hinz, Michael 5 Howard, Peter 5 Hussein, Amru 5 Ignat, Liviu I. 5 Kairzhan, Adilbek 5 Katsevich, Alexander I. 5 Kerner, Joachim 5 Kiselev, Alexander V. 5 Knudsen, Kim M. 5 Kostenko, Aleksey S. 5 Marzuola, Jeremy L. 5 Monard, François ...and 1,328 more Authors
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### Cited in 270 Serials

 65 Inverse Problems 64 Journal of Mathematical Analysis and Applications 55 Journal of Mathematical Physics 39 Communications in Mathematical Physics 32 Journal of Differential Equations 32 Annales Henri Poincaré 30 Journal of Functional Analysis 27 SIAM Journal on Imaging Sciences 24 Integral Equations and Operator Theory 23 SIAM Journal on Mathematical Analysis 21 Journal of Mathematical Sciences (New York) 20 Transactions of the American Mathematical Society 20 St. Petersburg Mathematical Journal 19 Journal of Computational Physics 18 Letters in Mathematical Physics 17 Analysis and Mathematical Physics 16 Inverse Problems and Imaging 15 Archive for Rational Mechanics and Analysis 15 Reviews in Mathematical Physics 14 Functional Analysis and its Applications 13 Applicable Analysis 13 Communications in Partial Differential Equations 13 Russian Journal of Mathematical Physics 13 Journal of Inverse and Ill-Posed Problems 12 SIAM Journal on Applied Mathematics 11 Journal d’Analyse Mathématique 11 Mathematical Notes 11 Proceedings of the American Mathematical Society 11 Calculus of Variations and Partial Differential Equations 10 Journal of Computational and Applied Mathematics 10 Numerische Mathematik 10 The Journal of Fourier Analysis and Applications 10 Journal of Physics A: Mathematical and Theoretical 9 Journal of Statistical Physics 9 Reports on Mathematical Physics 9 Advances in Mathematics 9 Mathematische Nachrichten 9 Doklady Mathematics 9 Complex Analysis and Operator Theory 8 Israel Journal of Mathematics 8 Physics Letters. A 8 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 8 Inverse Problems in Science and Engineering 8 Networks and Heterogeneous Media 8 Journal of Spectral Theory 7 Mathematical Methods in the Applied Sciences 7 Annales de l’Institut Fourier 7 Results in Mathematics 7 Journal de Mathématiques Pures et Appliquées. Neuvième Série 7 Journal of Mathematical Imaging and Vision 7 Journal of Evolution Equations 7 Complex Variables and Elliptic Equations 6 Computers & Mathematics with Applications 6 Nonlinearity 6 ZAMP. Zeitschrift für angewandte Mathematik und Physik 6 Duke Mathematical Journal 6 European Journal of Applied Mathematics 6 Linear Algebra and its Applications 6 Journal of Nonlinear Science 6 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 6 Communications on Pure and Applied Analysis 5 Theoretical and Mathematical Physics 5 Journal of Geometry and Physics 5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 Physica D 5 Engineering Analysis with Boundary Elements 5 Discrete and Continuous Dynamical Systems 5 Mathematical Physics, Analysis and Geometry 5 Multiscale Modeling & Simulation 5 Waves in Random and Complex Media 5 Symmetry 4 Computer Methods in Applied Mechanics and Engineering 4 Applied Mathematics and Computation 4 SIAM Journal on Numerical Analysis 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 4 Applied Mathematics Letters 4 Applied and Computational Harmonic Analysis 4 NoDEA. Nonlinear Differential Equations and Applications 4 Opuscula Mathematica 4 Proceedings of the Steklov Institute of Mathematics 4 Operators and Matrices 4 Izvestiya Instituta Matematiki i Informatiki. Udmurtskiĭ Gosudarstvennyĭ Universitet 3 Russian Mathematical Surveys 3 Wave Motion 3 Arkiv för Matematik 3 Applied Mathematics and Optimization 3 Geometriae Dedicata 3 International Journal for Numerical Methods in Engineering 3 Journal of Soviet Mathematics 3 Mathematische Annalen 3 Quarterly of Applied Mathematics 3 Siberian Mathematical Journal 3 Transactions of the Moscow Mathematical Society 3 Optimization 3 Journal of Scientific Computing 3 The Journal of Geometric Analysis 3 Computational Mathematics and Mathematical Physics 3 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 3 Potential Analysis 3 Journal of Mathematical Chemistry ...and 170 more Serials
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### Cited in 57 Fields

 699 Partial differential equations (35-XX) 372 Quantum theory (81-XX) 284 Operator theory (47-XX) 208 Ordinary differential equations (34-XX) 196 Numerical analysis (65-XX) 133 Biology and other natural sciences (92-XX) 131 Optics, electromagnetic theory (78-XX) 129 Statistical mechanics, structure of matter (82-XX) 119 Integral transforms, operational calculus (44-XX) 94 Combinatorics (05-XX) 78 Global analysis, analysis on manifolds (58-XX) 66 Functional analysis (46-XX) 65 Mechanics of deformable solids (74-XX) 55 Information and communication theory, circuits (94-XX) 49 Calculus of variations and optimal control; optimization (49-XX) 44 Fluid mechanics (76-XX) 41 Dynamical systems and ergodic theory (37-XX) 32 Differential geometry (53-XX) 25 Probability theory and stochastic processes (60-XX) 23 Harmonic analysis on Euclidean spaces (42-XX) 23 Integral equations (45-XX) 21 Difference and functional equations (39-XX) 20 Systems theory; control (93-XX) 18 Computer science (68-XX) 15 Abstract harmonic analysis (43-XX) 14 Potential theory (31-XX) 13 Algebraic geometry (14-XX) 13 Several complex variables and analytic spaces (32-XX) 12 Measure and integration (28-XX) 10 Convex and discrete geometry (52-XX) 9 Manifolds and cell complexes (57-XX) 9 Operations research, mathematical programming (90-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 8 $$K$$-theory (19-XX) 8 Group theory and generalizations (20-XX) 8 Topological groups, Lie groups (22-XX) 8 Real functions (26-XX) 8 Approximations and expansions (41-XX) 7 Algebraic topology (55-XX) 7 Statistics (62-XX) 6 History and biography (01-XX) 6 Number theory (11-XX) 6 Functions of a complex variable (30-XX) 6 Classical thermodynamics, heat transfer (80-XX) 6 Geophysics (86-XX) 5 General and overarching topics; collections (00-XX) 5 Associative rings and algebras (16-XX) 4 Nonassociative rings and algebras (17-XX) 4 Geometry (51-XX) 4 Mechanics of particles and systems (70-XX) 3 Special functions (33-XX) 3 General topology (54-XX) 2 Category theory; homological algebra (18-XX) 1 Commutative algebra (13-XX) 1 Sequences, series, summability (40-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematics education (97-XX)