## Exner, Pavel

Compute Distance To:
 Author ID: exner.pavel Published as: Exner, Pavel; Exner, P. Homepage: http://gemma.ujf.cas.cz/~exner/ External Links: MGP · ORCID · Wikidata · Google Scholar · dblp · GND · IdRef · theses.fr
 Documents Indexed: 255 Publications since 1975, including 4 Books 12 Contributions as Editor · 1 Further Contribution Biographic References: 2 Publications Co-Authors: 104 Co-Authors with 223 Joint Publications 2,181 Co-Co-Authors
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### Co-Authors

 45 single-authored 27 Šeba, Petr 15 Tater, Miloš 14 Lotoreichik, Vladimir 13 Kondej, Sylwia 10 Barseghyan, Diana 10 Duclos, Pierre 10 Neidhardt, Hagen 10 Zagrebnov, Valentin A. 9 Dittrich, Jaroslav 9 Ichinose, Takashi 9 Lipovský, Jiří 9 Turek, Ondřej 8 Havlíček, Miloslav 7 Behrndt, Jussi 7 Fraas, Martin 6 Borisov, Denis Ivanovich 6 Kovařík, Hynek 6 Krejčiřík, David 5 Blank, Jiří 5 Cheon, Taksu 5 Post, Olaf 5 Vugal’ter, Semën Abramovich 4 Bentosela, François 4 Geyler, Vladimir A. 4 Holzmann, Markus 4 Manko, Stepan S. 4 Němcová, K. 4 Šťovíček, Pavel 4 Weidl, Timo 4 Yoshitomi, Kazushi 3 Albeverio, Sergio A. 3 Harrell, Evans M. II 3 Jex, Michal 3 Joye, Alain 3 Khrabustovskyi, Andrii 3 Kuchment, Peter A. 3 Lassner, Wolfgang 3 Malamud, Mark M. 3 Pankrashkin, Konstantin 2 Antoine, Jean-Pierre 2 Asch, Joachim 2 Brüning, Jochen 2 Burdík, Čestmír 2 Frank, Rupert L. 2 Gadyl’shin, Rustem R. 2 Gesztesy, Fritz 2 Hirokawa, Masao 2 Holden, Helge 2 Keating, Jonathan Peter 2 Kolerov, G. I. 2 Kostenko, Aleksey S. 2 Loss, Michael 2 Minakov, Alexander 2 Shabani, Juma 2 Stollmann, Peter 2 Sunada, Toshikazu 2 Teplyaev, Alexander 2 Vaněk, D. 2 Vašata, Daniel 1 Avron, Joseph E. 1 Bakharev, Fedor L’vovich 1 Baradaran, Marzieh 1 Brasche, Johannes Friedemann 1 Cacciapuoti, Claudio 1 Carlone, Raffaele 1 Carron, Gilles 1 Catto, Isabelle 1 Cavalcanti, R. M. 1 Davies, Edward Brian 1 Demuth, Michael 1 Dobrokhotov, Sergei Yurievich 1 Freitas, Pedro 1 Gawlista, R. 1 Golovina, Anastasiya Mihajlovna 1 Grébert, Benoît 1 Hainzl, Christian 1 Hejčík, Pavel 1 Helm, Mario 1 Høegh-Krohn, Raphael J. 1 Kalvoda, Tomáš 1 König, Wolfgang Dieter 1 Koshmanenko, Volodymyr Dmytrovych 1 Kreičiřík, D. 1 Kühn, Christian 1 Kuperin, Yuri A. 1 Laptev, Ari 1 Last, Yoram 1 Linde, Helmut 1 Mantile, Andrea 1 Meller, Bernhard 1 Navrátil, Ondřej 1 Ogurisu, Osamu 1 Parnovski, Leonid 1 Pavlov, Boris Sergeevich 1 Pérez-Obiol, Axel 1 Popov, Igor’ Yur’evich 1 Rohleder, Jonathan 1 Seifert, Christian 1 Šerešová, E. 1 Šovíček, P. ...and 5 more Co-Authors
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### Serials

 33 Journal of Mathematical Physics 24 Journal of Physics A: Mathematical and General 24 Journal of Physics A: Mathematical and Theoretical 19 Letters in Mathematical Physics 18 Physics Letters. A 14 Reports on Mathematical Physics 10 Annales Henri Poincaré 9 Reviews in Mathematical Physics 8 European Mathematical Society Newsletter 5 Integral Equations and Operator Theory 4 Communications in Mathematical Physics 3 Journal of Geometry and Physics 3 Annals of Physics 3 Annales de l’Institut Henri Poincaré. Physique Théorique 3 Operator Theory: Advances and Applications 2 Acta Universitatis Carolinae. Mathematica et Physica 2 Journal of Mathematical Analysis and Applications 2 Russian Journal of Mathematical Physics 2 Operators and Matrices 2 Theoretical and Mathematical Physics (Cham) 1 Helvetica Physica Acta 1 International Journal of Theoretical Physics 1 Journal of Statistical Physics 1 Waves in Random Media 1 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section A. Physique Théorique 1 Journal of the Mathematical Society of Japan 1 Mathematische Nachrichten 1 Asymptotic Analysis 1 Communications in Partial Differential Equations 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Bulletin of the American Mathematical Society. New Series 1 Doklady Mathematics 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Communications in Contemporary Mathematics 1 Physical Review Letters 1 Czechoslovak Journal of Physics 1 Portugaliae Mathematica. Nova Série 1 Journal of Mathematical Physics, Analysis, Geometry 1 Contemporary Mathematics 1 Fundamental Theories of Physics 1 Lecture Notes in Physics 1 Proceedings of the Steklov Institute of Mathematics 1 Proceedings of Symposia in Pure Mathematics 1 Journal of Spectral Theory 1 Afrika Matematika 1 Quantum Studies: Mathematics and Foundations 1 Nanosystems. Physics, Chemistry, Mathematics 1 EMS Series of Congress Reports
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### Fields

 225 Quantum theory (81-XX) 111 Partial differential equations (35-XX) 74 Operator theory (47-XX) 23 Functional analysis (46-XX) 22 Statistical mechanics, structure of matter (82-XX) 18 Ordinary differential equations (34-XX) 15 Global analysis, analysis on manifolds (58-XX) 14 General and overarching topics; collections (00-XX) 11 History and biography (01-XX) 9 Optics, electromagnetic theory (78-XX) 8 Combinatorics (05-XX) 8 Nonassociative rings and algebras (17-XX) 4 Measure and integration (28-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Approximations and expansions (41-XX) 3 Mechanics of particles and systems (70-XX) 2 Algebraic geometry (14-XX) 2 Associative rings and algebras (16-XX) 2 Geometry (51-XX) 2 Convex and discrete geometry (52-XX) 2 Differential geometry (53-XX) 2 Probability theory and stochastic processes (60-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Number theory (11-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Difference and functional equations (39-XX) 1 General topology (54-XX) 1 Numerical analysis (65-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Relativity and gravitational theory (83-XX)

### Citations contained in zbMATH Open

205 Publications have been cited 2,306 times in 959 Documents Cited by Year
Curvature-induced bound states in quantum waveguides in two and three dimensions. Zbl 0837.35037
Duclos, P.; Exner, P.
1995
Solvable models in quantum mechanics. With an appendix by Pavel Exner. 2nd revised ed. Zbl 1078.81003
Albeverio, Sergio; Gesztesy, Friedrich; Høegh-Krohn, Raphael; Holden, Helge
2005
Bound states in curved quantum waveguides. Zbl 0693.46066
Exner, P.; Seba, P.
1989
Schrödinger operators with singular interactions. Zbl 0820.47005
Brasche, J. F.; Exner, P.; Kuperin, Yu. A.; Šeba, P.
1994
Hilbert space operators in quantum physics. 2nd ed. Zbl 1163.47060
Blank, Jiří; Exner, Pavel; Havlíček, Miloslav
2008
Quantum waveguides. Zbl 1314.81001
Exner, Pavel; Kovařík, Hynek
2015
Leaky quantum graphs: a review. Zbl 1153.81487
Exner, Pavel
2008
Convergence of spectra of graph-like thin manifolds. Zbl 1095.58007
Exner, Pavel; Post, Olaf
2005
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
Geometrically induced spectrum in curved leaky wires. Zbl 1002.81024
Exner, P.; Ichinose, T.
2001
Bound states and scattering in quantum waveguides coupled laterally through a boundary window. Zbl 0883.35085
Exner, P.; Šeba, P.; Tater, M.; Vaněk, D.
1996
Bound states in curved quantum layers. Zbl 0988.81034
Duclos, P.; Exner, P.; Krejčiřík, D.
2001
Open quantum systems and Feynman integrals. Zbl 0638.46051
Exner, Pavel
1985
Topologically nontrivial quantum layers. Zbl 1070.58025
Carron, G.; Exner, P.; Krejčiřík, D.
2004
Contact interactions on graph superlattices. Zbl 0916.47056
Exner, Pavel
1996
Dirac operators with a spherically symmetric $$\delta$$-shell interaction. Zbl 0694.46053
Dittrich, J.; Exner, P.; Šeba, P.
1989
Bound states in weakly deformed strips and layers. Zbl 1043.35046
Borisov, D.; Exner, P.; Gadyl’shin, R.; Krejčiřík, D.
2001
Geometric coupling thresholds in a two-dimensional strip. Zbl 1060.35094
Borisov, D.; Exner, P.; Gadyl’shin, R.
2002
Asymptotics of eigenvalues of the Schrödinger operator with a strong $$\delta$$-interaction on a loop. Zbl 1083.35034
Exner, Pavel; Yoshitomi, Kazushi
2002
Free quantum motion on a branching graph. Zbl 0749.47038
Exner, P.; Šeba, P.
1989
Bound states due to a strong $$\delta$$ interaction supported by a curved surface. Zbl 1050.81009
Exner, P.; Kondej, S.
2003
Periodic Schrödinger operators with large gaps and Wannier-Stark ladders. Zbl 0942.34503
Avron, J. E.; Exner, P.; Last, Y.
1994
Schrödinger operators with $$\delta$$- and $$\delta'$$-interactions on Lipschitz surfaces and chromatic numbers of associated partitions. Zbl 1326.47050
Behrndt, Jussi; Exner, Pavel; Lotoreichik, Vladimir
2014
A duality between Schrödinger operators on graphs and certain Jacobi matrices. Zbl 0949.34073
Exner, P.
1997
Asymptotic eigenvalue estimates for a Robin problem with a large parameter. Zbl 1295.35346
Exner, Pavel; Minakov, Alexander; Parnovski, Leonid
2014
Curvature-induced bound states for a $$\delta$$ interaction supported by a curve in $$\mathbb{R}^3$$. Zbl 1017.81007
Exner, P.; Kondej, S.
2002
Exponential splitting of bound states in a waveguide with a pair of distant windows. Zbl 1050.81008
Borisov, D.; Exner, P.
2004
Approximation of quantum graph vertex couplings by scaled Schrödinger operators on thin branched manifolds. Zbl 1179.81080
Exner, Pavel; Post, Olaf
2009
Bound-state asymptotic estimates for window-coupled Dirichlet strips and layers. Zbl 0930.58016
Exner, Pavel; Vugalter, Simeon A.
1997
Bound states in a locally deformed waveguide: The critical case. Zbl 0871.35067
Exner, P.; Vugalter, S. A.
1997
Schrödinger operators with $$\delta$$-interactions supported on conical surfaces. Zbl 1297.35154
Behrndt, J.; Exner, P.; Lotoreichik, V.
2014
Approximation of a general singular vertex coupling in quantum graphs. Zbl 1192.81159
Cheon, Taksu; Exner, Pavel; Turek, Ondřej
2010
Potential approximations to $$\delta'$$: an inverse Klauder phenomenon with norm-resolvent convergence. Zbl 1161.81375
Exner, Pavel; Neidhardt, Hagen; Zagrebnov, Valentin A.
2002
On the ground state of quantum graphs with attractive $$\delta$$-coupling. Zbl 1255.81160
Exner, Pavel; Jex, Michal
2012
On the spectral properties of Dirac operators with electrostatic $$\delta$$-shell interactions. Zbl 1382.81095
Behrndt, Jussi; Exner, Pavel; Holzmann, Markus; Lotoreichik, Vladimir
2018
On the location of spectral edges in $$\mathbb Z$$-periodic media. Zbl 1204.81063
Exner, Pavel; Kuchment, Peter; Winn, Brian
2010
Weakly coupled states on branching graphs. Zbl 0861.35068
Exner, Pavel
1996
Stability of driven systems with growing gaps, quantum rings, and Wannier ladders. Zbl 1079.81518
Asch, Joachim; Duclos, Pierre; Exner, Pavel
1998
Scattering by local deformations of a straight leaky wire. Zbl 1071.81027
Exner, P.; Kondej, S.
2005
Leaky quantum graphs: Approximations by point-interaction Hamiltonians. Zbl 1116.81312
Exner, P.; Němcová, K.
2003
The absence of the absolutely continuous spectrum for $$\delta'$$ Wannier-Stark ladders. Zbl 0884.47049
Exner, P.
1995
Asymptotic estimates for bound states in quantum waveguides coupled laterally through a narrow window. Zbl 0858.35093
Exner, P.; Vugalter, S. A.
1996
Spectrum of the Schrödinger operator in a perturbed periodically twisted tube. Zbl 1111.35014
Exner, P.; Kovařík, H.
2005
Nontrivial edge coupling from a Dirichlet network squeezing: the case of a bent waveguide. Zbl 1136.81442
Cacciapuoti, Claudio; Exner, Pavel
2007
A general approximation of quantum graph vertex couplings by scaled Schrödinger operators on thin branched manifolds. Zbl 1270.81099
Exner, Pavel; Post, Olaf
2013
On Dirac operators in $$\mathbb{R}^3$$ with electrostatic and Lorentz scalar $$\delta$$-shell interactions. Zbl 1423.81072
Behrndt, Jussi; Exner, Pavel; Holzmann, Markus; Lotoreichik, Vladimir
2019
Spectral theory of infinite quantum graphs. Zbl 1476.81047
Exner, Pavel; Kostenko, Aleksey; Malamud, Mark; Neidhardt, Hagen
2018
Hiatus perturbation for a singular Schrödinger operator with an interaction supported by a curve in $$\mathbb R^{3}$$. Zbl 1153.81356
Exner, P.; Kondej, S.
2008
Optimal eigenvalues for some Laplacians and Schrödinger operators depending on curvature. Zbl 0971.58018
Exner, Pavel; Harrell, Evans M.; Loss, Michael
1999
Large gaps in point-coupled periodic systems of manifolds. Zbl 1057.81023
Brüning, Jochen; Exner, Pavel; Geyler, Vladimir A.
2003
Strong coupling asymptotics for a singular Schrödinger operator with an interaction supported by an open arc. Zbl 1291.35247
Exner, Pavel; Pankrashkin, Konstantin
2014
Generalized interactions supported on hypersurfaces. Zbl 1339.81038
Exner, Pavel; Rohleder, Jonathan
2016
On the spectrum of a bent chain graph. Zbl 1192.81167
Duclos, Pierre; Exner, Pavel; Turek, Ondřej
2008
Inequalities for means of chords, with application to isoperimetric problems. Zbl 1111.35019
Exner, Pavel; Harrell, Evans M.; Loss, Michael
2006
Dirac Hamiltonian with Coulomb potential and spherically symmetric shell contact interaction. Zbl 0761.35071
Dittrich, J.; Exner, P.; Šeba, P.
1992
Non-Weyl asymptotics for quantum graphs with general coupling conditions. Zbl 1204.81078
Davies, E. Brian; Exner, Pavel; Lipovský, Jiří
2010
Spectrum of Dirichlet Laplacian in a conical layer. Zbl 1204.81064
Exner, Pavel; Tater, Miloš
2010
Approximation of Schrödinger operators with {$$\delta$$}-interactions supported on hypersurfaces. Zbl 1376.35010
Behrndt, Jussi; Exner, Pavel; Holzmann, Markus; Lotoreichik, Vladimir
2017
Resonance statistics in a microwave cavity with a thin antenna. Zbl 0962.78501
Exner, P.; Šeba, P.
1997
Band gap of the Schrödinger operator with a strong $$\delta$$-interaction on a periodic curve. Zbl 1035.81020
Exner, P.; Yoshitomi, K.
2001
An approximation to $$\delta'$$ couplings on graphs. Zbl 1062.81017
Cheon, T.; Exner, P.
2004
An isoperimetric problem for point interactions. Zbl 1070.81049
Exner, Pavel
2005
Curvature-induced bound states in Robin waveguides and their asymptotical properties. Zbl 1315.81045
Exner, Pavel; Minakov, Alexander
2014
Open quantum dots: Resonances from perturbed symmetry and bound states in strong magnetic fields. Zbl 0976.81006
Duclos, Pierre; Exner, Pavel; Meller, Bernhard
2001
On geometric perturbations of critical Schrödinger operators with a surface interaction. Zbl 1300.81034
Exner, Pavel; Fraas, Martin
2009
Resonances from perturbations of quantum graphs with rationally related edges. Zbl 1192.81160
Exner, Pavel; Lipovský, Jiří
2010
Hilbert space operators in quantum physics. Zbl 0873.46038
Blank, Jiří; Exner, Pavel; Havlíček, Miloslav
1994
Quantum motion on a half-line connected to a plane. Zbl 0634.46057
Exner, P.; Šeba, P.
1987
Persistent currents for the 2D Schrödinger operator with a strong $$\delta$$-interaction on a loop. Zbl 1010.81012
Exner, P.; Yoshitomi, K.
2002
Distant perturbation asymptotics in window-coupled waveguides. I: The nonthreshold case. Zbl 1112.81043
Borisov, D.; Exner, P.
2006
Strong-coupling asymptotic expansion for Schrödinger operators with a singular interaction supported by a curve in $$\mathbb{R}^3$$. Zbl 1053.81030
Exner, P.; Kondej, S.
2004
Generalized boundary conditions for the Aharonov-Bohm effect combined with a homogeneous magnetic field. Zbl 1059.81056
Exner, P.; Šťovíček, P.; Vytřas, P.
2002
Spectra of soft ring graphs. Zbl 1063.81534
Exner, P.; Tater, M.
2004
Localization on a quantum graph with a random potential on the edges. Zbl 1147.82018
Exner, Pavel; Helm, Mario; Stollmann, Peter
2007
Periodic quantum graphs from the Bethe-Sommerfeld perspective. Zbl 1383.81090
Exner, Pavel; Turek, Ondřej
2017
Magnetic strip waveguides. Zbl 0954.81011
Exner, Pavel; Kovařík, Hynek
2000
Bound states in quantum waveguides of a slowly decaying curvature. Zbl 0767.35051
Exner, Pavel
1993
A product formula related to quantum zeno dynamics. Zbl 1092.81004
Exner, Pavel; Ichinose, Takashi
2005
A spectral isoperimetric inequality for cones. Zbl 1360.35207
2017
Absolute continuity in periodic thin tubes and strongly coupled leaky wires. Zbl 1038.81018
Bentosela, Francois; Duclos, Pierre; Exner, Pavel
2003
Anomalous electron trapping by localized magnetic fields. Zbl 1055.81522
Bentosela, F.; Cavalcanti, R. M.; Exner, P.; Zagrebnov, V. A.
1999
A quantum pipette. Zbl 0868.81001
Exner, Pavel
1995
An isoperimetric problem for leaky loops and related mean-chord inequalities. Zbl 1110.81076
Exner, Pavel
2005
Tunneling through a singular potential barrier. Zbl 0578.47013
Dittrich, J.; Exner, P.
1985
A mathematical model of heavy-quarkonia mesonic decays. Zbl 0828.58042
Antoine, J.-P.; Exner, P.; Šeba, P.; Shabani, J.
1994
Point interactions in a strip. Zbl 0891.47052
Exner, P.; Gawlista, R.; Šeba, P.; Tater, M.
1996
Bound states in mildly curved layers. Zbl 0981.81022
Exner, P.; Krejčiřík, D.
2001
Lieb-Thirring inequalities on trapped modes in quantum wires. Zbl 1039.81021
Exner, Pavel; Weidl, Timo
2001
Schrödinger operators with singular interactions: a model of tunnelling resonances. Zbl 1072.81056
Exner, P.; Kondej, S.
2004
A lower bound to the spectral threshold in curved tubes. Zbl 1330.35360
Exner, P.; Freitas, P.; Krejčiřík, D.
2004
On resonances and bound states of Smilansky Hamiltonian. Zbl 1366.81163
Exner, P.; Lotoreichik, V.; Tater, M.
2016
On eigenvalue asymptotics for strong $$\delta$$-interactions supported by surfaces with boundaries. Zbl 1398.35138
Dittrich, Jaroslav; Exner, Pavel; Kühn, Christian; Pankrashkin, Konstantin
2016
Momentum operators on graphs. Zbl 1325.05105
Exner, Pavel
2013
Absence of absolutely continuous spectrum for the Kirchhoff Laplacian on radial trees. Zbl 1292.81061
Exner, Pavel; Seifert, Christian; Stollmann, Peter
2014
Approximations of quantum-graph vertex couplings by singularly scaled rank-one operators. Zbl 1300.81045
Exner, Pavel; Manko, Stepan S.
2014
Remarks on the Trotter-Kato product formula for unitary groups. Zbl 1228.47042
Exner, Pavel; Neidhardt, Hagen; Zagrebnov, Valentin A.
2011
Quantum networks modelled by graphs. Zbl 1180.81028
Exner, Pavel; Post, Olaf
2008
Point interactions in two and three dimensions as models of small scatterers. Zbl 0972.81532
Exner, P.; Šeba, P.
1996
Electrons in semiconductor microstructures: A challenge to operator theorists. Zbl 0736.35130
Exner, Pavel; Šeba, Petr
1989
Exponential bounds on curvature-induced resonances in a two-dimensional Dirichlet tube. Zbl 1080.35506
Duclos, P.; Exner, P.
1998
Corrigendum to: “Note on a product formula related to quantum Zeno dynamics”. Zbl 07348131
Exner, Pavel; Ichinose, Takashi
2021
Ring chains with vertex coupling of a preferred orientation. Zbl 07409547
Baradaran, Marzieh; Exner, Pavel; Tater, Miloš
2021
The Landau Hamiltonian with $$\delta$$-potentials supported on curves. Zbl 1465.35132
Behrndt, Jussi; Exner, Pavel; Holzmann, Markus; Lotoreichik, Vladimir
2020
Spectral asymptotics of the Dirichlet Laplacian on a generalized parabolic layer. Zbl 1439.35355
2020
Topological bulk-edge effects in quantum graph transport. Zbl 1448.81326
Exner, Pavel; Lipovský, Jiří
2020
Spectral optimization for strongly singular Schrödinger operators with a star-shaped interaction. Zbl 1436.81045
Exner, P.; Kondej, S.
2020
On Dirac operators in $$\mathbb{R}^3$$ with electrostatic and Lorentz scalar $$\delta$$-shell interactions. Zbl 1423.81072
Behrndt, Jussi; Exner, Pavel; Holzmann, Markus; Lotoreichik, Vladimir
2019
Spectral asymptotics of the Laplacian on platonic solids graphs. Zbl 1431.81063
Exner, Pavel; Lipovský, Jiří
2019
On the spectral properties of Dirac operators with electrostatic $$\delta$$-shell interactions. Zbl 1382.81095
Behrndt, Jussi; Exner, Pavel; Holzmann, Markus; Lotoreichik, Vladimir
2018
Spectral theory of infinite quantum graphs. Zbl 1476.81047
Exner, Pavel; Kostenko, Aleksey; Malamud, Mark; Neidhardt, Hagen
2018
On the bound states of magnetic Laplacians on wedges. Zbl 1441.35181
Exner, Pavel; Lotoreichik, Vladimir; Pérez-Obiol, Axel
2018
Quantum graphs with vertices of a preferred orientation. Zbl 1387.81223
Exner, Pavel; Tater, Miloš
2018
Aharonov and Bohm versus Welsh eigenvalues. Zbl 1396.81090
Exner, P.; Kondej, S.
2018
Asymptotics of the bound state induced by $$\delta$$-interaction supported on a weakly deformed plane. Zbl 1380.81118
Exner, Pavel; Kondej, Sylwia; Lotoreichik, Vladimir
2018
Optimization of the lowest eigenvalue for leaky star graphs. Zbl 1461.35169
2018
Gap control by singular Schrödinger operators in a periodically structured metamaterial. Zbl 1423.35263
Exner, Pavel; Khrabustovskyi, Andrii
2018
A family of quantum graph vertex couplings interpolating between different symmetries. Zbl 1396.81098
Exner, Pavel; Turek, Ondřej; Tater, Miloš
2018
Smilansky-Solomyak model with a $$\delta^\prime$$-interaction. Zbl 1383.81094
Exner, Pavel; Lipovský, Jiří
2018
A geometric Iwatsuka type effect in quantum layers. Zbl 1386.81156
Exner, Pavel; Kalvoda, Tomáš; Tušek, Matěj
2018
On the spectrum of leaky surfaces with a potential bias. Zbl 1398.35136
Exner, Pavel
2018
Geometrically induced spectral effects in tubes with a mixed Dirichlet-Neumann boundary. Zbl 1402.81162
Bakharev, Fedor L.; Exner, Pavel
2018
Approximation of Schrödinger operators with {$$\delta$$}-interactions supported on hypersurfaces. Zbl 1376.35010
Behrndt, Jussi; Exner, Pavel; Holzmann, Markus; Lotoreichik, Vladimir
2017
Periodic quantum graphs from the Bethe-Sommerfeld perspective. Zbl 1383.81090
Exner, Pavel; Turek, Ondřej
2017
A spectral isoperimetric inequality for cones. Zbl 1360.35207
2017
Spectral and resonance properties of the Smilansky Hamiltonian. Zbl 1372.81041
Exner, Pavel; Lotoreichik, Vladimir; Tater, Miloš
2017
A magnetic version of the Smilansky-Solomyak model. Zbl 1380.81115
Barseghyan, Diana; Exner, Pavel
2017
Pseudo-orbit approach to trajectories of resonances in quantum graphs with general vertex coupling: Fermi rule and high-energy asymptotics. Zbl 1360.81169
Exner, Pavel; Lipovský, Jiří
2017
Cantor spectra of magnetic chain graphs. Zbl 1368.82003
Exner, Pavel; Vašata, Daniel
2017
Spectral properties of magnetic chain graphs. Zbl 1370.81075
Exner, Pavel; Manko, Stepan
2017
A regular analogue of the Smilansky model: spectral properties. Zbl 1384.81023
Barseghyan, Diana; Exner, Pavel
2017
Infinite quantum graphs. Zbl 1365.05177
Kostenko, A. S.; Malamud, M. M.; Neidhardt, H.; Exner, P.
2017
Generalized interactions supported on hypersurfaces. Zbl 1339.81038
Exner, Pavel; Rohleder, Jonathan
2016
On resonances and bound states of Smilansky Hamiltonian. Zbl 1366.81163
Exner, P.; Lotoreichik, V.; Tater, M.
2016
On eigenvalue asymptotics for strong $$\delta$$-interactions supported by surfaces with boundaries. Zbl 1398.35138
Dittrich, Jaroslav; Exner, Pavel; Kühn, Christian; Pankrashkin, Konstantin
2016
Strong coupling asymptotics for Schrödinger operators with an interaction supported by an open arc in three dimensions. Zbl 1378.81032
Exner, Pavel; Kondej, Sylwia
2016
Spectral analysis of a class of Schrödinger operators exhibiting a parameter-dependent spectral transition. Zbl 1344.81085
Barseghyan, Diana; Exner, Pavel; Khrabustovskyi, Andrii; Tater, Miloš
2016
Semiclassical bounds in magnetic bottles. Zbl 1335.81072
Barseghyan, Diana; Exner, Pavel; Kovařík, Hynek; Weidl, Timo
2016
On the existence of bound states in asymmetric leaky wires. Zbl 1332.81070
Exner, Pavel; Vugalter, Semjon
2016
Quantum waveguides. Zbl 1314.81001
Exner, Pavel; Kovařík, Hynek
2015
Gap asymptotics in a weakly bent leaky quantum wire. Zbl 1330.81101
Exner, Pavel; Kondej, Sylwia
2015
Spectrum of a dilated honeycomb network. Zbl 1318.81027
Exner, Pavel; Turek, Ondřej
2015
Spectra of magnetic chain graphs: coupling constant perturbations. Zbl 1309.05092
Exner, Pavel; Manko, Stepan S.
2015
On the spectrum of narrow Neumann waveguide with periodically distributed $$\delta^\prime$$ traps. Zbl 1325.81091
Exner, Pavel; Khrabustovskyi, Andrii
2015
Schrödinger operators with $$\delta$$- and $$\delta'$$-interactions on Lipschitz surfaces and chromatic numbers of associated partitions. Zbl 1326.47050
Behrndt, Jussi; Exner, Pavel; Lotoreichik, Vladimir
2014
Asymptotic eigenvalue estimates for a Robin problem with a large parameter. Zbl 1295.35346
Exner, Pavel; Minakov, Alexander; Parnovski, Leonid
2014
Schrödinger operators with $$\delta$$-interactions supported on conical surfaces. Zbl 1297.35154
Behrndt, J.; Exner, P.; Lotoreichik, V.
2014
Strong coupling asymptotics for a singular Schrödinger operator with an interaction supported by an open arc. Zbl 1291.35247
Exner, Pavel; Pankrashkin, Konstantin
2014
Curvature-induced bound states in Robin waveguides and their asymptotical properties. Zbl 1315.81045
Exner, Pavel; Minakov, Alexander
2014
Absence of absolutely continuous spectrum for the Kirchhoff Laplacian on radial trees. Zbl 1292.81061
Exner, Pavel; Seifert, Christian; Stollmann, Peter
2014
Approximations of quantum-graph vertex couplings by singularly scaled rank-one operators. Zbl 1300.81045
Exner, Pavel; Manko, Stepan S.
2014
On some sharp spectral inequalities for Schrödinger operators on semiaxis. Zbl 1297.35155
Exner, Pavel; Laptev, Ari; Usman, Muhammad
2014
Spectral asymptotics of a strong $$\delta'$$ interaction supported by a surface. Zbl 1331.81093
Exner, Pavel; Jex, Michal
2014
Spectral estimates for Dirichlet Laplacians on perturbed twisted tubes. Zbl 1288.81047
Exner, Pavel; Barseghyan, Diana
2014
Book review of: Gregory Berkolaiko and Peter Kuchment, Introduction to quantum graphs. Zbl 1301.00028
Exner, Pavel
2014
A general approximation of quantum graph vertex couplings by scaled Schrödinger operators on thin branched manifolds. Zbl 1270.81099
Exner, Pavel; Post, Olaf
2013
Momentum operators on graphs. Zbl 1325.05105
Exner, Pavel
2013
Tunneling resonances in systems without a classical trapping. Zbl 1280.81035
Borisov, D.; Exner, P.; Golovina, A.
2013
Spectral asymptotics of a strong $$\delta^{\prime}$$ interaction on a planar loop. Zbl 1273.81088
Exner, Pavel; Jex, Michal
2013
Solvable models of resonances and decays. Zbl 1266.81094
Exner, Pavel
2013
Approximations of quantum-graph vertex couplings by singularly scaled potentials. Zbl 1278.81095
Exner, Pavel; Manko, Stepan S.
2013
Spectral estimates for Dirichlet Laplacians and Schrödinger operators on geometrically nontrivial cusps. Zbl 1294.35043
Barseghyan, Diana; Exner, Pavel
2013
On the ground state of quantum graphs with attractive $$\delta$$-coupling. Zbl 1255.81160
Exner, Pavel; Jex, Michal
2012
Spectral estimates for a class of Schrödinger operators with infinite phase space and potential unbounded from below. Zbl 1241.81072
Exner, Pavel; Barseghyan, Diana
2012
Remarks on the Trotter-Kato product formula for unitary groups. Zbl 1228.47042
Exner, Pavel; Neidhardt, Hagen; Zagrebnov, Valentin A.
2011
Dynamics of an electron confined to a “hybrid plane” and interacting with a magnetic field. Zbl 1239.81039
Carlone, Raffaele; Exner, Pavel
2011
Non-Weyl resonance asymptotics for quantum graphs in a magnetic field. Zbl 1241.81078
Exner, Pavel; Lipovský, Jiří
2011
Vertex couplings in quantum graphs: approximations by scaled Schrödinger operators. Zbl 1264.81214
Exner, Pavel
2011
Approximation of a general singular vertex coupling in quantum graphs. Zbl 1192.81159
Cheon, Taksu; Exner, Pavel; Turek, Ondřej
2010
On the location of spectral edges in $$\mathbb Z$$-periodic media. Zbl 1204.81063
Exner, Pavel; Kuchment, Peter; Winn, Brian
2010
Non-Weyl asymptotics for quantum graphs with general coupling conditions. Zbl 1204.81078
Davies, E. Brian; Exner, Pavel; Lipovský, Jiří
2010
Spectrum of Dirichlet Laplacian in a conical layer. Zbl 1204.81064
Exner, Pavel; Tater, Miloš
2010
Resonances from perturbations of quantum graphs with rationally related edges. Zbl 1192.81160
Exner, Pavel; Lipovský, Jiří
2010
High-energy asymptotics of the spectrum of a periodic square lattice quantum graph. Zbl 1204.81065
Exner, Pavel; Turek, Ondřej
2010
On the absence of absolutely continuous spectra for Schrödinger operators on radial tree graphs. Zbl 1314.81086
Exner, Pavel; Lipovský, Jiří
2010
Tripartite connection condition for a quantum graph vertex. Zbl 1241.81056
Cheon, Taksu; Exner, Pavel; Turek, Ondřej
2010
Approximation of quantum graph vertex couplings by scaled Schrödinger operators on thin branched manifolds. Zbl 1179.81080
Exner, Pavel; Post, Olaf
2009
On geometric perturbations of critical Schrödinger operators with a surface interaction. Zbl 1300.81034
Exner, Pavel; Fraas, Martin
2009
Hilbert space operators in quantum physics. 2nd ed. Zbl 1163.47060
Blank, Jiří; Exner, Pavel; Havlíček, Miloslav
2008
Leaky quantum graphs: a review. Zbl 1153.81487
Exner, Pavel
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
Hiatus perturbation for a singular Schrödinger operator with an interaction supported by a curve in $$\mathbb R^{3}$$. Zbl 1153.81356
Exner, P.; Kondej, S.
2008
On the spectrum of a bent chain graph. Zbl 1192.81167
Duclos, Pierre; Exner, Pavel; Turek, Ondřej
2008
Quantum networks modelled by graphs. Zbl 1180.81028
Exner, Pavel; Post, Olaf
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 optimization of the principal eigenvalue for single-centre point-interaction operators in a bounded region. Zbl 1135.81014
Exner, Pavel; Mantile, Andrea
2008
Interlaced dense point and absolutely continuous spectra for Hamiltonians with concentric-shell singular interactions. Zbl 1156.81383
Exner, Pavel; Fraas, Martin
2008
Nontrivial edge coupling from a Dirichlet network squeezing: the case of a bent waveguide. Zbl 1136.81442
Cacciapuoti, Claudio; Exner, Pavel
2007
Localization on a quantum graph with a random potential on the edges. Zbl 1147.82018
Exner, Pavel; Helm, Mario; Stollmann, Peter
2007
On the critical exponent in an isoperimetric inequality for chords. Zbl 1209.35090
Exner, Pavel; Fraas, Martin; Harrell, Evans M. II
2007
A “hybrid plane” with spin-orbit interaction. Zbl 1175.81092
Exner, P.; Šeba, P.
2007
On the dense point and absolutely continuous spectrum for Hamiltonians with concentric $$\delta$$ shells. Zbl 1136.35019
Exner, Pavel; Fraas, Martin
2007
Zeno product formula revisited. Zbl 1119.47016
Exner, Pavel; Ichinose, Takashi; Neidhardt, Hagen; Zagrebnov, Valentin A.
2007
Absolute continuity of the spectrum for periodically modulated leaky wires in $${\mathbb{R}^{3}}$$. Zbl 1206.82112
Exner, Pavel; Frank, Rupert L.
2007
The decay law can have an irregular character. Zbl 1109.81013
Exner, Pavel; Fraas, Martin
2007
Equivalence of resolvent and scattering resonances on quantum graphs. Zbl 1137.81010
Exner, Pavel; Lipovskýy, Jiří
2007
Convergence of resonances on thin branched quantum waveguides. Zbl 1152.81426
Exner, Pavel; Post, Olaf
2007
Unstable system dynamics: do we understand it fully? Zbl 1159.81010
Exner, Pavel
2007
On relations between stable and Zeno dynamics in a leaky graph decay model. Zbl 1122.81031
Exner, Pavel; Ichinose, Takashi; Kondej, Sylwia
2007
Approximations of singular vertex couplings in quantum graphs. Zbl 1148.81011
Exner, Pavel; Turek, Ondřej
2007
Inequalities for means of chords, with application to isoperimetric problems. Zbl 1111.35019
Exner, Pavel; Harrell, Evans M.; Loss, Michael
2006
...and 105 more Documents
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### Cited by 828 Authors

 96 Exner, Pavel 36 Nazarov, Sergeĭ Aleksandrovich 35 Borisov, Denis Ivanovich 34 Pankrashkin, Konstantin 32 Krejčiřík, David 28 Lotoreichik, Vladimir 20 Popov, Igor’ Yur’evich 17 Behrndt, Jussi 17 Kovařík, Hynek 16 Kurasov, Pavel B. 16 Raymond, Nicolas 15 Albeverio, Sergio A. 15 Kondej, Sylwia 14 Post, Olaf 12 Cacciapuoti, Claudio 12 Neidhardt, Hagen 11 Malamud, Mark M. 11 Ourmiéres-Bonafos, Thomas 11 Rabinovich, Vladimir Samuilovich 10 Briet, Philippe 10 Cardone, Giuseppe 10 Kerner, Joachim 10 Kostenko, Aleksey S. 9 Adami, Riccardo 9 Berkolaiko, Gregory 9 Popoff, Nicolas 9 Posilicano, Andrea 9 Rohleder, Jonathan 9 Siegl, Petr 8 Barseghyan, Diana 8 Brüning, Jochen 8 Geyler, Vladimir A. 8 Holzmann, Markus 8 Turek, Ondřej 8 Veselić, Ivan 7 Bakharev, Fedor L’vovich 7 Duclos, Pierre 7 Freitas, Pedro 7 Kachmar, Ayman 7 Lipovský, Jiří 7 Mas, Albert 7 Mugnolo, Delio 7 Niikuni, Hiroaki 7 Tater, Miloš 7 Vugal’ter, Semën Abramovich 6 Dauge, Monique 6 Dovetta, Simone 6 Finco, Domenico 6 Golovina, Anastasiya Mihajlovna 6 Hounkonnou, Mahouton Norbert 6 Joye, Alain 6 Khimshiashvili, Giorgi 6 Mantile, Andrea 6 Yang, Chuanfu 5 Angulo Pava, Jaime 5 Arrizabalaga, Naiara 5 Blinova, Irina V. 5 Craster, Richard V. 5 Ekholm, Tomas 5 Frank, Rupert L. 5 Gadyl’shin, Rustem R. 5 Harrell, Evans M. II 5 Janda, Jiří 5 Kennedy, James Bernard 5 Khrabustovskyi, Andrii 5 Kiselev, Alexander V. 5 Kuchment, Peter A. 5 Laptev, Ari 5 Lenz, Daniel H. 5 Lu, Zhiqin 5 Nenciu, Gheorghe 5 Nicolussi, Noema 5 Noja, Diego 5 Pelinovsky, Dmitry Efimovich 5 Riečanová, Zdenka 5 Šeba, Petr 5 Serra, Enrico 5 Soccorsi, Eric 5 Šťovíček, Pavel 5 Tušek, Matěj 5 Verri, Alessandra A. 5 Weidl, Timo 4 Avossevou, Gabriel Y. H. 4 Band, Ram 4 Bikmetov, Aĭdar Renatovich 4 Bondarenko, Natalia P. 4 Brasche, Johannes Friedemann 4 Bunoiu, Renata 4 Carlone, Raffaele 4 Cheon, Taksu 4 Cherednichenko, Kirill D. 4 Dobrokhotov, Sergei Yurievich 4 Facchi, Paolo 4 Goloshchapova, Nataliia 4 Grushin, V. V. 4 Havlíček, Miloslav 4 Kairzhan, Adilbek 4 Karabash, Illya M. 4 Konyrkulzhaeva, Maral Nurlanovna 4 Lampart, Jonas ...and 728 more Authors
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### Cited in 211 Serials

 125 Journal of Mathematical Physics 42 Journal of Mathematical Analysis and Applications 35 Annales Henri Poincaré 34 Journal of Functional Analysis 28 Reviews in Mathematical Physics 27 Communications in Mathematical Physics 27 Reports on Mathematical Physics 26 Journal of Differential Equations 24 Letters in Mathematical Physics 23 Journal of Mathematical Sciences (New York) 19 Physics Letters. A 18 Integral Equations and Operator Theory 18 Journal of Physics A: Mathematical and Theoretical 15 Russian Journal of Mathematical Physics 14 Journal of Spectral Theory 13 St. Petersburg Mathematical Journal 11 Mathematical Notes 11 Theoretical and Mathematical Physics 10 International Journal of Theoretical Physics 9 Applicable Analysis 9 Journal of Statistical Physics 9 ZAMP. Zeitschrift für angewandte Mathematik und Physik 9 Journal de Mathématiques Pures et Appliquées. Neuvième Série 9 Calculus of Variations and Partial Differential Equations 9 Mathematical Physics, Analysis and Geometry 8 Advances in Mathematics 8 Proceedings of the American Mathematical Society 8 Transactions of the American Mathematical Society 8 Communications in Partial Differential Equations 7 Mathematische Nachrichten 6 Journal of Geometry and Physics 6 Annales de l’Institut Henri Poincaré. Physique Théorique 6 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 6 Operators and Matrices 5 Wave Motion 5 Archiv der Mathematik 5 The Journal of Geometric Analysis 5 SIAM Journal on Mathematical Analysis 5 Doklady Mathematics 5 Analysis and Mathematical Physics 4 Archive for Rational Mechanics and Analysis 4 Journal of Fluid Mechanics 4 Annals of Physics 4 Foundations of Physics 4 Complex Variables and Elliptic Equations 4 Complex Analysis and Operator Theory 3 Modern Physics Letters B 3 Mathematical Methods in the Applied Sciences 3 Annales de l’Institut Fourier 3 Mathematika 3 Publications of the Research Institute for Mathematical Sciences, Kyoto University 3 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 3 Applied Mathematics Letters 3 Asymptotic Analysis 3 Linear Algebra and its Applications 3 Journal of Inverse and Ill-Posed Problems 3 Sbornik: Mathematics 3 Journal of Mathematical Chemistry 3 Communications in Contemporary Mathematics 3 Journal of Evolution Equations 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Waves in Random and Complex Media 3 Proceedings of the Steklov Institute of Mathematics 3 Networks and Heterogeneous Media 3 Bulletin of the Georgian National Academy of Sciences. New Series 3 Symmetry 3 Quantum Studies: Mathematics and Foundations 2 Bulletin of the Australian Mathematical Society 2 Inverse Problems 2 Journal of Computational Physics 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Nonlinearity 2 Nuclear Physics. B 2 Arkiv för Matematik 2 Applied Mathematics and Computation 2 Functional Analysis and its Applications 2 Mathematische Annalen 2 Mathematische Zeitschrift 2 Memoirs of the American Mathematical Society 2 Results in Mathematics 2 Siberian Mathematical Journal 2 Zeitschrift für Analysis und ihre Anwendungen 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Revista Matemática Iberoamericana 2 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 SIAM Journal on Applied Mathematics 2 Journal of Inequalities and Applications 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 New Journal of Physics 2 Lobachevskii Journal of Mathematics 2 Gravitation & Cosmology 2 Portugaliae Mathematica. Nova Série 2 Journal of Applied Mathematics and Computing 2 Quantum Information Processing 2 International Journal of Geometric Methods in Modern Physics 2 Foundations of Physics Letters 2 Mathematical Modelling of Natural Phenomena 2 Analysis & PDE 2 Studies in History and Philosophy of Science. Part B. Studies in History and Philosophy of Modern Physics ...and 111 more Serials
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### Cited in 54 Fields

 571 Quantum theory (81-XX) 472 Partial differential equations (35-XX) 288 Operator theory (47-XX) 141 Ordinary differential equations (34-XX) 99 Statistical mechanics, structure of matter (82-XX) 75 Global analysis, analysis on manifolds (58-XX) 52 Functional analysis (46-XX) 49 Combinatorics (05-XX) 49 Optics, electromagnetic theory (78-XX) 25 Calculus of variations and optimal control; optimization (49-XX) 24 Probability theory and stochastic processes (60-XX) 21 Differential geometry (53-XX) 19 Mechanics of deformable solids (74-XX) 18 Numerical analysis (65-XX) 17 Dynamical systems and ergodic theory (37-XX) 17 Fluid mechanics (76-XX) 14 Mechanics of particles and systems (70-XX) 13 Nonassociative rings and algebras (17-XX) 13 Measure and integration (28-XX) 11 Relativity and gravitational theory (83-XX) 10 Order, lattices, ordered algebraic structures (06-XX) 9 Approximations and expansions (41-XX) 8 Difference and functional equations (39-XX) 7 Functions of a complex variable (30-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 7 Convex and discrete geometry (52-XX) 6 Mathematical logic and foundations (03-XX) 6 Potential theory (31-XX) 6 Geometry (51-XX) 5 Number theory (11-XX) 5 Real functions (26-XX) 5 Biology and other natural sciences (92-XX) 4 Algebraic geometry (14-XX) 4 Manifolds and cell complexes (57-XX) 4 Statistics (62-XX) 4 Information and communication theory, circuits (94-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Group theory and generalizations (20-XX) 3 Topological groups, Lie groups (22-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Special functions (33-XX) 3 Integral equations (45-XX) 3 Geophysics (86-XX) 3 Systems theory; control (93-XX) 2 Abstract harmonic analysis (43-XX) 2 Integral transforms, operational calculus (44-XX) 2 Operations research, mathematical programming (90-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 General algebraic systems (08-XX) 1 Associative rings and algebras (16-XX) 1 Algebraic topology (55-XX) 1 Computer science (68-XX) 1 Classical thermodynamics, heat transfer (80-XX)

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