Lagacé, Jean; Morozov, Sergey; Parnovski, Leonid; Pfirsch, Bernhard; Shterenberg, Roman The almost periodic gauge transform: an abstract scheme with applications to Dirac operators. (La Transformée de Jauge presque priodique : une méthode abstraite et ses applications aux opérateurs de Dirac.) (English. French summary) Zbl 07814463 Ann. Henri Lebesgue 6, 1031-1113 (2023). MSC: 35P20 35J46 47A55 81Q10 PDFBibTeX XMLCite \textit{J. Lagacé} et al., Ann. Henri Lebesgue 6, 1031--1113 (2023; Zbl 07814463) Full Text: DOI arXiv
Chesnel, Lucas; Nazarov, Sergei A. Spectrum of the Dirichlet Laplacian in a thin cubic lattice. (English) Zbl 07792486 ESAIM, Math. Model. Numer. Anal. 57, No. 6, 3251-3273 (2023). MSC: 35P20 35J05 35Q40 47A75 81Q37 PDFBibTeX XMLCite \textit{L. Chesnel} and \textit{S. A. Nazarov}, ESAIM, Math. Model. Numer. Anal. 57, No. 6, 3251--3273 (2023; Zbl 07792486) Full Text: DOI arXiv
Kuchment, Peter Analytic and algebraic properties of dispersion relations (Bloch varieties) and Fermi surfaces. What is known and unknown. (English) Zbl 07774862 J. Math. Phys. 64, No. 11, Article ID 113504, 11 p. (2023). MSC: 35P05 81Q10 47F05 PDFBibTeX XMLCite \textit{P. Kuchment}, J. Math. Phys. 64, No. 11, Article ID 113504, 11 p. (2023; Zbl 07774862) Full Text: DOI arXiv
Gómez, Delfina; Nazarov, Sergei A.; Orive-Illera, Rafael; Pérez-Martínez, María-Eugenia Asymptotic stability of the spectrum of a parametric family of homogenization problems associated with a perforated waveguide. (English) Zbl 1525.35018 Math. Nachr. 296, No. 10, 4888-4910 (2023). MSC: 35B27 35P05 35J25 47A10 47A55 PDFBibTeX XMLCite \textit{D. Gómez} et al., Math. Nachr. 296, No. 10, 4888--4910 (2023; Zbl 1525.35018) Full Text: DOI arXiv OA License
Bessonov, R.; Denisov, S. Szegő condition, scattering, and vibration of Krein strings. (English) Zbl 07749818 Invent. Math. 234, No. 1, 291-373 (2023). MSC: 47-XX PDFBibTeX XMLCite \textit{R. Bessonov} and \textit{S. Denisov}, Invent. Math. 234, No. 1, 291--373 (2023; Zbl 07749818) Full Text: DOI arXiv
Cancedda, Andrea; Chiadó Piat, Valeria; Nazarov, Sergei A.; Taskinen, Jari Spectral gaps for the linear water-wave problem in a channel with thin structures. (English) Zbl 1523.35131 Math. Nachr. 295, No. 4, 657-682 (2022). MSC: 35J05 35J25 35P15 47A10 PDFBibTeX XMLCite \textit{A. Cancedda} et al., Math. Nachr. 295, No. 4, 657--682 (2022; Zbl 1523.35131) Full Text: DOI OA License
Ben-Artzi, Jonathan; Marletta, Marco; Rösler, Frank Universal algorithms for computing spectra of periodic operators. (English) Zbl 1486.35157 Numer. Math. 150, No. 3, 719-767 (2022). MSC: 35J10 47B37 35P05 37A10 68Q25 PDFBibTeX XMLCite \textit{J. Ben-Artzi} et al., Numer. Math. 150, No. 3, 719--767 (2022; Zbl 1486.35157) Full Text: DOI arXiv
Borisov, D. I. On lacunas in the spectrum of the Laplacian with the Dirichlet boundary condition in a band with oscillating boundary. (English. Russian original) Zbl 1471.35211 J. Math. Sci., New York 257, No. 3, 273-285 (2021); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 162, 3-14 (2019). MSC: 35P15 35B27 35J25 47A10 PDFBibTeX XMLCite \textit{D. I. Borisov}, J. Math. Sci., New York 257, No. 3, 273--285 (2021; Zbl 1471.35211); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 162, 3--14 (2019) Full Text: DOI
Fillman, Jake; Han, Rui Discrete Bethe-Sommerfeld conjecture for triangular, square, and hexagonal lattices. (English) Zbl 07308598 J. Anal. Math. 142, No. 1, 271-321 (2020). MSC: 47Axx 37Nxx 11Pxx 37Axx 82Cxx PDFBibTeX XMLCite \textit{J. Fillman} and \textit{R. Han}, J. Anal. Math. 142, No. 1, 271--321 (2020; Zbl 07308598) Full Text: DOI arXiv
Nazarov, S. A. Threshold resonances and virtual levels in the spectrum of cylindrical and periodic waveguides. (English. Russian original) Zbl 1458.35031 Izv. Math. 84, No. 6, 1105-1160 (2020); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 84, No. 6, 73-130 (2020). MSC: 35B25 35P05 35Q60 47A53 78A50 82D77 PDFBibTeX XMLCite \textit{S. A. Nazarov}, Izv. Math. 84, No. 6, 1105--1160 (2020; Zbl 1458.35031); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 84, No. 6, 73--130 (2020) Full Text: DOI
Leugering, Günter; Nazarov, Sergei A.; Taskinen, Jari The band-gap structure of the spectrum in a periodic medium of masonry type. (English) Zbl 1454.35130 Netw. Heterog. Media 15, No. 4, 555-580 (2020). MSC: 35J57 35P99 47B25 PDFBibTeX XMLCite \textit{G. Leugering} et al., Netw. Heterog. Media 15, No. 4, 555--580 (2020; Zbl 1454.35130) Full Text: DOI
Viorel, Catană \(S\)-operators related to a finite measure space. (English) Zbl 1513.47070 Appl. Anal. 99, No. 2, 326-339 (2020). MSC: 47B38 42A16 47G30 46E30 42C10 PDFBibTeX XMLCite \textit{C. Viorel}, Appl. Anal. 99, No. 2, 326--339 (2020; Zbl 1513.47070) Full Text: DOI
Nazarov, S. A. Finite-dimensional approximations to the Poincaré-Steklov operator for general elliptic boundary value problems in domains with cylindrical and periodic exits to infinity. (English. Russian original) Zbl 1445.35157 Trans. Mosc. Math. Soc. 2019, 1-51 (2019); translation from Tr. Mosk. Mat. O.-va 80, No. 1, 1-62 (2019). Reviewer: Rodica Luca (Iaşi) MSC: 35J57 47F05 PDFBibTeX XMLCite \textit{S. A. Nazarov}, Trans. Mosc. Math. Soc. 2019, 1--51 (2019; Zbl 1445.35157); translation from Tr. Mosk. Mat. O.-va 80, No. 1, 1--62 (2019) Full Text: DOI
Nazarov, Sergei A.; Orive-Illera, Rafael; Pérez-Martínez, María-Eugenia Asymptotic structure of the spectrum in a Dirichlet-strip with double periodic perforations. (English) Zbl 1435.35267 Netw. Heterog. Media 14, No. 4, 733-757 (2019). Reviewer: Denis Borisov (Ufa) MSC: 35P05 35B27 47A55 35J25 47A10 35P10 35P15 47A75 PDFBibTeX XMLCite \textit{S. A. Nazarov} et al., Netw. Heterog. Media 14, No. 4, 733--757 (2019; Zbl 1435.35267) Full Text: DOI
Embree, Mark; Fillman, Jake Spectra of discrete two-dimensional periodic Schrödinger operators with small potentials. (English) Zbl 1436.35095 J. Spectr. Theory 9, No. 3, 1063-1087 (2019). Reviewer: Andreas Kleefeld (Jülich) MSC: 35J10 47B36 PDFBibTeX XMLCite \textit{M. Embree} and \textit{J. Fillman}, J. Spectr. Theory 9, No. 3, 1063--1087 (2019; Zbl 1436.35095) Full Text: DOI arXiv
Hou, Xuanji; Shan, Yuan; You, Jiangong Construction of quasiperiodic Schrödinger operators with Cantor spectrum. (English) Zbl 1430.37027 Ann. Henri Poincaré 20, No. 11, 3563-3601 (2019). Reviewer: Namig Guliyev (Baku) MSC: 37C45 47A10 34L05 34L40 PDFBibTeX XMLCite \textit{X. Hou} et al., Ann. Henri Poincaré 20, No. 11, 3563--3601 (2019; Zbl 1430.37027) Full Text: DOI
Karpeshina, Yulia; Shterenberg, Roman Extended states for the Schrödinger operator with quasi-periodic potential in dimension two. (English) Zbl 1442.35003 Memoirs of the American Mathematical Society 1239. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-3543-1/pbk; 978-1-4704-5069-4/ebook). v, 139 p. (2019). MSC: 35-02 35J10 35P15 35P20 81Q05 81Q10 81Q15 37K55 47F05 PDFBibTeX XMLCite \textit{Y. Karpeshina} and \textit{R. Shterenberg}, Extended states for the Schrödinger operator with quasi-periodic potential in dimension two. Providence, RI: American Mathematical Society (AMS) (2019; Zbl 1442.35003) Full Text: DOI arXiv
Damanik, David; Fillman, Jake; Gorodetski, Anton Multidimensional almost-periodic Schrödinger operators with Cantor spectrum. (English) Zbl 1474.34608 Ann. Henri Poincaré 20, No. 4, 1393-1402 (2019). MSC: 34L40 47A11 PDFBibTeX XMLCite \textit{D. Damanik} et al., Ann. Henri Poincaré 20, No. 4, 1393--1402 (2019; Zbl 1474.34608) Full Text: DOI arXiv
Catană, Viorel \( \mathbb{Z} \)-operators related to a finite measure space. (English) Zbl 1441.47043 J. Pseudo-Differ. Oper. Appl. 9, No. 2, 173-188 (2018). Reviewer: Luis Filipe Pinheiro de Castro (Aveiro) MSC: 47B38 42A16 47G30 46E30 42C10 PDFBibTeX XMLCite \textit{V. Catană}, J. Pseudo-Differ. Oper. Appl. 9, No. 2, 173--188 (2018; Zbl 1441.47043) Full Text: DOI
Han, Rui; Jitomirskaya, Svetlana Discrete Bethe-Sommerfeld conjecture. (English) Zbl 1403.35190 Commun. Math. Phys. 361, No. 1, 205-216 (2018). Reviewer: Vassilis G. Papanicolaou (Athena) MSC: 35P20 81Q10 35J10 47G30 PDFBibTeX XMLCite \textit{R. Han} and \textit{S. Jitomirskaya}, Commun. Math. Phys. 361, No. 1, 205--216 (2018; Zbl 1403.35190) Full Text: DOI arXiv
Exner, Pavel; Turek, Ondřej Periodic quantum graphs from the Bethe-Sommerfeld perspective. (English) Zbl 1383.81090 J. Phys. A, Math. Theor. 50, No. 45, Article ID 455201, 32 p. (2017). Reviewer: Jonathan Rohleder (Hamburg) MSC: 81Q35 47A10 11K60 PDFBibTeX XMLCite \textit{P. Exner} and \textit{O. Turek}, J. Phys. A, Math. Theor. 50, No. 45, Article ID 455201, 32 p. (2017; Zbl 1383.81090) Full Text: DOI arXiv
Bakharev, F. L.; Cardone, G.; Nazarov, S. A.; Taskinen, J. Effects of Rayleigh waves on the essential spectrum in perturbed doubly periodic elliptic problems. (English) Zbl 1386.35280 Integral Equations Oper. Theory 88, No. 3, 373-386 (2017). MSC: 35P05 47A75 PDFBibTeX XMLCite \textit{F. L. Bakharev} et al., Integral Equations Oper. Theory 88, No. 3, 373--386 (2017; Zbl 1386.35280) Full Text: DOI arXiv Link
Nguyen, Van Kien; Ullrich, Mario; Ullrich, Tino Change of variable in spaces of mixed smoothness and numerical integration of multivariate functions on the unit cube. (English) Zbl 1376.65028 Constr. Approx. 46, No. 1, 69-108 (2017). Reviewer: Manfred Tasche (Rostock) MSC: 65D32 41A55 41A63 46E35 47B38 PDFBibTeX XMLCite \textit{V. K. Nguyen} et al., Constr. Approx. 46, No. 1, 69--108 (2017; Zbl 1376.65028) Full Text: DOI arXiv
Parnovski, Leonid; Shterenberg, Roman Perturbation theory for spectral gap edges of 2D periodic Schrödinger operators. (English) Zbl 1386.35308 J. Funct. Anal. 273, No. 1, 444-470 (2017). Reviewer: Rodica Luca (Iaşi) MSC: 35P20 35J10 47A55 81Q10 PDFBibTeX XMLCite \textit{L. Parnovski} and \textit{R. Shterenberg}, J. Funct. Anal. 273, No. 1, 444--470 (2017; Zbl 1386.35308) Full Text: DOI arXiv
Cardone, G.; Durante, T.; Nazarov, S. A. The spectrum, radiation conditions and the Fredholm property for the Dirichlet Laplacian in a perforated plane with semi-infinite inclusions. (English) Zbl 1386.35281 J. Differ. Equations 263, No. 2, 1387-1418 (2017). Reviewer: Jonathan Rohleder (Hamburg) MSC: 35P05 47A75 49R05 78A50 PDFBibTeX XMLCite \textit{G. Cardone} et al., J. Differ. Equations 263, No. 2, 1387--1418 (2017; Zbl 1386.35281) Full Text: DOI arXiv
Simonov, Sergey Zeroes of the spectral density of the Schrödinger operator with the slowly decaying Wigner-von Neumann potential. (English) Zbl 1372.47059 Math. Z. 284, No. 1-2, 335-411 (2016). Reviewer: Ekin Uğurlu (Ankara) MSC: 47E05 34B20 34L40 PDFBibTeX XMLCite \textit{S. Simonov}, Math. Z. 284, No. 1--2, 335--411 (2016; Zbl 1372.47059) Full Text: DOI arXiv
Kuchment, Peter An overview of periodic elliptic operators. (English) Zbl 1346.35170 Bull. Am. Math. Soc., New Ser. 53, No. 3, 343-414 (2016). Reviewer: Boris A. Malomed (Tel Aviv) MSC: 35Q40 35J10 35J15 47A53 47F05 58J05 PDFBibTeX XMLCite \textit{P. Kuchment}, Bull. Am. Math. Soc., New Ser. 53, No. 3, 343--414 (2016; Zbl 1346.35170) Full Text: DOI arXiv
Cuenin, Jean-Claude; Tretter, Christiane Non-symmetric perturbations of self-adjoint operators. (English) Zbl 1341.47017 J. Math. Anal. Appl. 441, No. 1, 235-258 (2016). MSC: 47A55 47B25 47A10 PDFBibTeX XMLCite \textit{J.-C. Cuenin} and \textit{C. Tretter}, J. Math. Anal. Appl. 441, No. 1, 235--258 (2016; Zbl 1341.47017) Full Text: DOI arXiv
Cardone, G.; Nazarov, S. A.; Taskinen, J. Spectra of open waveguides in periodic media. (English) Zbl 1322.35097 J. Funct. Anal. 269, No. 8, 2328-2364 (2015). Reviewer: Dumitru Motreanu (Perpignan) MSC: 35P05 47A75 49R05 78A50 PDFBibTeX XMLCite \textit{G. Cardone} et al., J. Funct. Anal. 269, No. 8, 2328--2364 (2015; Zbl 1322.35097) Full Text: DOI arXiv
El Aïdi, Mohammed On the number of negative eigenvalues of an elliptic operator. (Sur le nombre des valeurs propres négatives d’un opérateur elliptique.) (French. English summary) Zbl 1286.35178 Bull. Sci. Math. 137, No. 4, 434-456 (2013). Reviewer: Denis A. White (Toledo) MSC: 35P15 35J40 47A75 47F05 PDFBibTeX XMLCite \textit{M. El Aïdi}, Bull. Sci. Math. 137, No. 4, 434--456 (2013; Zbl 1286.35178) Full Text: DOI
Kordyukov, Yu. A.; Yakovlev, A. A. Integer points in domains and adiabatic limits. (English. Russian original) Zbl 1290.11134 St. Petersbg. Math. J. 23, No. 6, 977-987 (2012); translation from Algebra Anal. 23, No. 6, 80-95 (2011). MSC: 11P21 34L20 35J10 47A75 52C07 58C40 81Q20 PDFBibTeX XMLCite \textit{Yu. A. Kordyukov} and \textit{A. A. Yakovlev}, St. Petersbg. Math. J. 23, No. 6, 977--987 (2012; Zbl 1290.11134); translation from Algebra Anal. 23, No. 6, 80--95 (2011) Full Text: DOI arXiv
Kuchment, Peter; Raich, Andrew Green’s function asymptotics near the internal edges of spectra of periodic elliptic operators: Spectral edge case. (English) Zbl 1257.35080 Math. Nachr. 285, No. 14-15, 1880-1894 (2012). Reviewer: James Bernard Kennedy (Ulm) MSC: 35J08 35J15 35P05 47A10 47F05 47N20 PDFBibTeX XMLCite \textit{P. Kuchment} and \textit{A. Raich}, Math. Nachr. 285, No. 14--15, 1880--1894 (2012; Zbl 1257.35080) Full Text: DOI arXiv
El Aïdi, Mohammed Un majorant du nombre des valeurs propres négatives correspondantes à l’opérateur de Schrödinger généralisé. (An upper bound on the number of negative eigenvalues of the generalised Schrödinger operator.) (French. English summary) Zbl 1256.35034 Ann. Math. Blaise Pascal 19, No. 1, 197-211 (2012). Reviewer: Thierry Jecko (Cergy-Pontoise) MSC: 35P15 35J10 47F05 PDFBibTeX XMLCite \textit{M. El Aïdi}, Ann. Math. Blaise Pascal 19, No. 1, 197--211 (2012; Zbl 1256.35034) Full Text: DOI
Naboko, Serguei; Simonov, Sergey Zeroes of the spectral density of the periodic Schrödinger operator with Wigner-von Neumann potential. (English) Zbl 1257.34072 Math. Proc. Camb. Philos. Soc. 153, No. 1, 33-58 (2012). Reviewer: Mihai Pascu (Bucureşti) MSC: 34L40 47A10 47E05 34B20 34L05 PDFBibTeX XMLCite \textit{S. Naboko} and \textit{S. Simonov}, Math. Proc. Camb. Philos. Soc. 153, No. 1, 33--58 (2012; Zbl 1257.34072) Full Text: DOI arXiv
Vorobets, Mariya On the Bethe-Sommerfeld conjecture for certain periodic Maxwell operators. (English) Zbl 1213.47055 J. Math. Anal. Appl. 377, No. 1, 370-383 (2011). Reviewer: Mihai Pascu (Bucureşti) MSC: 47G30 47A10 35Q61 35J10 35P20 PDFBibTeX XMLCite \textit{M. Vorobets}, J. Math. Anal. Appl. 377, No. 1, 370--383 (2011; Zbl 1213.47055) Full Text: DOI arXiv
Molahajloo, Shahla; Wong, M. W. Ellipticity, Fredholmness and spectral invariance of pseudo-differential operators on \({{\mathbb S}^1}\). (English) Zbl 1222.47075 J. Pseudo-Differ. Oper. Appl. 1, No. 2, 183-205 (2010). Reviewer: Anatoly N. Kochubei (Kyïv) MSC: 47G30 47A53 PDFBibTeX XMLCite \textit{S. Molahajloo} and \textit{M. W. Wong}, J. Pseudo-Differ. Oper. Appl. 1, No. 2, 183--205 (2010; Zbl 1222.47075) Full Text: DOI
Parnovski, Leonid; Sobolev, Alexander V. Bethe-Sommerfeld conjecture for periodic operators with strong perturbations. (English) Zbl 1200.47067 Invent. Math. 181, No. 3, 467-540 (2010). Reviewer: Michael Perelmuter (Kyïv) MSC: 47G30 35P20 47A55 81Q10 PDFBibTeX XMLCite \textit{L. Parnovski} and \textit{A. V. Sobolev}, Invent. Math. 181, No. 3, 467--540 (2010; Zbl 1200.47067) Full Text: DOI arXiv
Barbatis, G.; Parnovski, L. Bethe-Sommerfeld conjecture for pseudodifferential perturbation. (English) Zbl 1185.35349 Commun. Partial Differ. Equations 34, No. 4, 383-418 (2009). Reviewer: N. G. Tomin (Ivanovo) MSC: 35S05 35P20 58J40 58J50 47G30 PDFBibTeX XMLCite \textit{G. Barbatis} and \textit{L. Parnovski}, Commun. Partial Differ. Equations 34, No. 4, 383--418 (2009; Zbl 1185.35349) Full Text: DOI arXiv
Parnovski, Leonid; Shterenberg, Roman Asymptotic expansion of the integrated density of states of a two-dimensional periodic Schrödinger operator. (English) Zbl 1171.35092 Invent. Math. 176, No. 2, 275-323 (2009). Reviewer: Thierry Jecko (Cergy-Pontoise) MSC: 35P20 35J10 47A55 47G30 81Q10 PDFBibTeX XMLCite \textit{L. Parnovski} and \textit{R. Shterenberg}, Invent. Math. 176, No. 2, 275--323 (2009; Zbl 1171.35092) Full Text: DOI arXiv
Karpeshina, Yulia; Lee, Young-Ran Absolutely continuous spectrum of a polyharmonic operator with a limit periodic potential in dimension two. (English) Zbl 1151.35060 Commun. Partial Differ. Equations 33, No. 9, 1711-1728 (2008). MSC: 35P05 47F05 PDFBibTeX XMLCite \textit{Y. Karpeshina} and \textit{Y.-R. Lee}, Commun. Partial Differ. Equations 33, No. 9, 1711--1728 (2008; Zbl 1151.35060) Full Text: DOI arXiv
Yafaev, D. R. The Schrödinger operator: Perturbation determinants, the spectral shift function, trace identities, and all that. (English) Zbl 1222.47072 Funct. Anal. Appl. 41, No. 3, 217-236 (2007); translation from Funkts. Anal. Prilozh. 41, No. 3, 60-83 (2007). Reviewer: Wolfgang Sprößig (Freiberg) MSC: 47F05 35P20 PDFBibTeX XMLCite \textit{D. R. Yafaev}, Funct. Anal. Appl. 41, No. 3, 217--236 (2007; Zbl 1222.47072); translation from Funkts. Anal. Prilozh. 41, No. 3, 60--83 (2007) Full Text: DOI
Karpeshina, Yulia; Lee, Young-Ran Spectral properties of polyharmonic operators with limit-periodic potential in dimension two. (English) Zbl 1145.31001 J. Anal. Math. 102, 225-310 (2007). Reviewer: Ajay Kumar (Delhi) MSC: 31A99 47L30 PDFBibTeX XMLCite \textit{Y. Karpeshina} and \textit{Y.-R. Lee}, J. Anal. Math. 102, 225--310 (2007; Zbl 1145.31001) Full Text: DOI arXiv
Last, Yoram; Simon, Barry The essential spectrum of Schrödinger, Jacobi, and CMV operators. (English) Zbl 1145.34052 J. Anal. Math. 98, 183-220 (2006). Reviewer: Chuan-Fu Yang (Nanjing) MSC: 34L05 35P05 47A10 PDFBibTeX XMLCite \textit{Y. Last} and \textit{B. Simon}, J. Anal. Math. 98, 183--220 (2006; Zbl 1145.34052) Full Text: DOI arXiv
Pankrashkin, Konstantin Spectra of Schrödinger operators on equilateral quantum graphs. (English) Zbl 1113.81056 Lett. Math. Phys. 77, No. 2, 139-154 (2006). MSC: 81Q10 05C90 47A10 47N50 47F05 PDFBibTeX XMLCite \textit{K. Pankrashkin}, Lett. Math. Phys. 77, No. 2, 139--154 (2006; Zbl 1113.81056) Full Text: DOI arXiv
Shterenberg, R. G. On the structure of the lower edge of the spectrum of the periodic magnetic Schrödinger operator with small magnetic potential. (English. Russian original) Zbl 1264.35102 St. Petersbg. Math. J. 17, No. 5, 865-873 (2006); translation from Algebra Anal. 17, No. 5, 232-243 (2005). MSC: 35J10 35P05 35Q60 47F05 47N50 81Q10 PDFBibTeX XMLCite \textit{R. G. Shterenberg}, St. Petersbg. Math. J. 17, No. 5, 865--873 (2006; Zbl 1264.35102); translation from Algebra Anal. 17, No. 5, 232--243 (2005) Full Text: DOI
Skriganov, M. M.; Sobolev, A. V. On the spectrum of a limit-periodic Schrödinger operator. (English. Russian original) Zbl 1264.31006 St. Petersbg. Math. J. 17, No. 5, 815-833 (2006); translation from Algebra Anal. 17, No. 5, 164-189 (2005). MSC: 31B30 35J40 35P05 47F05 PDFBibTeX XMLCite \textit{M. M. Skriganov} and \textit{A. V. Sobolev}, St. Petersbg. Math. J. 17, No. 5, 815--833 (2006; Zbl 1264.31006); translation from Algebra Anal. 17, No. 5, 164--189 (2005) Full Text: DOI
Karpeshina, Yulia Spectral properties of the periodic magnetic Schrödinger operator in the high-energy region. Two-dimensional case. (English) Zbl 1059.81058 Commun. Math. Phys. 251, No. 3, 473-514 (2004). MSC: 81Q10 35P15 35P20 47N50 PDFBibTeX XMLCite \textit{Y. Karpeshina}, Commun. Math. Phys. 251, No. 3, 473--514 (2004; Zbl 1059.81058) Full Text: DOI
Damanik, David; Hundertmark, Dirk; Simon, Barry Bound states and the Szegő condition for Jacobi matrices and Schrödinger operators. (English) Zbl 1049.47032 J. Funct. Anal. 205, No. 2, 357-379 (2003). Reviewer: Michael Perelmuter (Kyïv) MSC: 47B36 47F05 PDFBibTeX XMLCite \textit{D. Damanik} et al., J. Funct. Anal. 205, No. 2, 357--379 (2003; Zbl 1049.47032) Full Text: DOI arXiv
Klopp, Frédéric; Wolff, Thomas Lifshitz tails for 2-dimensional random Schrödinger operators. (English) Zbl 1058.47034 J. Anal. Math. 88, 63-147 (2002). Reviewer: Francois Germinet (Villeneuve d’Ascq) MSC: 47B80 82B44 PDFBibTeX XMLCite \textit{F. Klopp} and \textit{T. Wolff}, J. Anal. Math. 88, 63--147 (2002; Zbl 1058.47034) Full Text: DOI
Klopp, Frédéric Lifshitz tails for random perturbations of periodic Schrödinger operators. (English) Zbl 0999.60089 Proc. Indian Acad. Sci., Math. Sci. 112, No. 1, 147-162 (2002). Reviewer: Kun Soo Chang (Seoul) MSC: 60K40 82B44 47B80 47N55 PDFBibTeX XMLCite \textit{F. Klopp}, Proc. Indian Acad. Sci., Math. Sci. 112, No. 1, 147--162 (2002; Zbl 0999.60089) Full Text: DOI
Karpeshina, Yu. E. On spectral properties of periodic polyharmonic matrix operators. (English) Zbl 1199.47195 Proc. Indian Acad. Sci., Math. Sci. 112, No. 1, 117-130 (2002). MSC: 47F05 35B10 35J10 35Q40 47N50 81Q10 PDFBibTeX XMLCite \textit{Yu. E. Karpeshina}, Proc. Indian Acad. Sci., Math. Sci. 112, No. 1, 117--130 (2002; Zbl 1199.47195) Full Text: DOI
Klopp, Frédéric Internal Lifshits tails for random perturbations of periodic Schrödinger operators. (English) Zbl 1060.82509 Duke Math. J. 98, No. 2, 335-396 (1999); correction ibid. 109, No. 2, 411-412 (2001). Reviewer: Jean-Michel Ghez (MR 2000m:82029) MSC: 82B44 47N55 81Q10 47B80 PDFBibTeX XMLCite \textit{F. Klopp}, Duke Math. J. 98, No. 2, 335--396 (2001; Zbl 1060.82509) Full Text: DOI
Helffer, Bernard; Mohamed, Abderemane Asymptotic of the density of states for the Schrödinger operator with periodic electric potential. (English) Zbl 0951.35104 Duke Math. J. 92, No. 1, 1-60 (1998). Reviewer: Viorel Iftimie (Bucureşti) MSC: 35P20 47F05 47N50 81Q10 35J10 PDFBibTeX XMLCite \textit{B. Helffer} and \textit{A. Mohamed}, Duke Math. J. 92, No. 1, 1--60 (1998; Zbl 0951.35104) Full Text: DOI
Gérard, Christian; Nier, Francis The Mourre theory for analytically fibered operators. (English) Zbl 0939.47019 J. Funct. Anal. 152, No. 1, 202-219 (1998). Reviewer: J.J.Telega (Warszawa) MSC: 47B25 81Q05 PDFBibTeX XMLCite \textit{C. Gérard} and \textit{F. Nier}, J. Funct. Anal. 152, No. 1, 202--219 (1998; Zbl 0939.47019) Full Text: DOI
Chuburin, Yu. P. On small perturbations of the Schrödinger operator with a periodic potential. (English. Russian original) Zbl 0913.47013 Theor. Math. Phys. 110, No. 3, 351-359 (1997); translation from Teor. Mat. Fiz. 110, No. 3, 443-453 (1997). MSC: 47A55 47F05 81Q15 PDFBibTeX XMLCite \textit{Yu. P. Chuburin}, Theor. Math. Phys. 110, No. 3, 351--359 (1997; Zbl 0913.47013); translation from Teor. Mat. Fiz. 110, No. 3, 443--453 (1997) Full Text: DOI
Naboko, S. N.; Pushnitskij, A. B. Point spectrum on a continuous spectrum for weakly perturbed Stark type operators. (English. Russian original) Zbl 0871.47035 Funct. Anal. Appl. 29, No. 4, 248-257 (1995); translation from Funkts. Anal. Prilozh. 29, No. 4, 31-44 (1995). Reviewer: Hou Jinchuan (Linfen / Shanxi) MSC: 47E05 47A10 47A55 PDFBibTeX XMLCite \textit{S. N. Naboko} and \textit{A. B. Pushnitskij}, Funct. Anal. Appl. 29, No. 4, 248--257 (1995; Zbl 0871.47035); translation from Funkts. Anal. Prilozh. 29, No. 4, 31--44 (1995) Full Text: DOI
Boutet de Monvel-Berthier, Anne; Nenciu, Alexandrina; Nenciu, Gheorghe Perturbed periodic Hamiltonians: Essential spectrum and exponential decay of eigenfunctions. (English) Zbl 0848.35103 Lett. Math. Phys. 34, No. 2, 119-133 (1995). MSC: 35Q40 35P99 47N50 81Q10 PDFBibTeX XMLCite \textit{A. Boutet de Monvel-Berthier} et al., Lett. Math. Phys. 34, No. 2, 119--133 (1995; Zbl 0848.35103) Full Text: DOI
Colin de Verdière, Yves Sur les singularités de Van Hove génériques. (On generic Van Hove singularities). (French) Zbl 0773.47034 Mém. Soc. Math. Fr., Nouv. Sér. 46, 99-109 (1991). Reviewer: B.Helffer (Paris) MSC: 47F05 35J10 PDFBibTeX XMLCite \textit{Y. Colin de Verdière}, Mém. Soc. Math. Fr., Nouv. Sér. 46, 99--109 (1991; Zbl 0773.47034) Full Text: DOI Numdam EuDML
Karpeshina, Yu. E. Perturbation theory for a polyharmonic operator with nonsmooth periodic potential. (English. Russian original) Zbl 0724.47022 J. Sov. Math. 54, No. 3, 911-915 (1991); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 169, 76-83 (1988). MSC: 47F05 47A10 47A55 PDFBibTeX XMLCite \textit{Yu. E. Karpeshina}, J. Sov. Math. 54, No. 3, 911--915 (1991; Zbl 0724.47022); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 169, 76--83 (1988) Full Text: DOI
Veliev, O. A. Spectrum of multidimensional periodic operators. (English. Russian original) Zbl 0696.47003 J. Sov. Math. 49, No. 4, 1045-1058 (1990); translation from Teor. Funkts., Funkts. Anal. Prilozh. 49, 17-34 (1988). MSC: 47A10 47F05 35J10 35B25 34C25 PDFBibTeX XMLCite \textit{O. A. Veliev}, J. Sov. Math. 49, No. 4, 1045--1058 (1990; Zbl 0696.47003); translation from Teor. Funkts., Funkts. Anal. Prilozh. 49, 17--34 (1988) Full Text: DOI
Malozemov, L. A. Unstable points of the spectrum of a periodic difference operator. (English. Russian original) Zbl 0723.47030 Funct. Anal. Appl. 23, No. 4, 329-330 (1989); translation from Funkts. Anal. Prilozh. 23, No. 4, 87-88 (1989). MSC: 47B39 PDFBibTeX XMLCite \textit{L. A. Malozemov}, Funct. Anal. Appl. 23, No. 4, 329--330 (1989; Zbl 0723.47030); translation from Funkts. Anal. Prilozh. 23, No. 4, 87--88 (1989) Full Text: DOI
Gerard, C. Resonance theory in atom-surface scattering. (English) Zbl 0682.47003 Commun. Math. Phys. 126, No. 2, 263-290 (1989). MSC: 47A40 81U99 PDFBibTeX XMLCite \textit{C. Gerard}, Commun. Math. Phys. 126, No. 2, 263--290 (1989; Zbl 0682.47003) Full Text: DOI
Bulla, W.; Gesztesy, F.; Unterkofler, K. On relativistic energy band corrections in the presence of periodic potentials. (English) Zbl 0657.47029 Lett. Math. Phys. 15, No. 4, 313-324 (1988). Reviewer: P.C.Sinha MSC: 47B25 46N99 81T20 PDFBibTeX XMLCite \textit{W. Bulla} et al., Lett. Math. Phys. 15, No. 4, 313--324 (1988; Zbl 0657.47029) Full Text: DOI
Veliev, O. A. Asymptotic formulas for the eigenvalues of a periodic Schrödinger operator and the Bethe-Sommerfeld conjecture. (English. Russian original) Zbl 0638.47049 Funct. Anal. Appl. 21, No. 1-3, 87-100 (1987); translation from Funkts. Anal. Prilozh. 21, No. 2, 1-15 (1987). Reviewer: C.Badea-Simionescu MSC: 47F05 47A10 35J10 PDFBibTeX XMLCite \textit{O. A. Veliev}, Funct. Anal. Appl. 21, No. 1--3, 87--100 (1987; Zbl 0638.47049); translation from Funkts. Anal. Prilozh. 21, No. 2, 1--15 (1987) Full Text: DOI
Hempel, Rainer; Hinz, Andreas M.; Kalf, Hubert On the essential spectrum of Schrödinger operators with spherically symmetric potentials. (English) Zbl 0629.35028 Math. Ann. 277, 197-208 (1987). Reviewer: T.Ichinose MSC: 35J10 81Q10 47A10 47B25 PDFBibTeX XMLCite \textit{R. Hempel} et al., Math. Ann. 277, 197--208 (1987; Zbl 0629.35028) Full Text: DOI EuDML
Koplienko, L. S. Regularized spectral shift function for one-dimensional Schrödinger operator with slowly decreasing potential. (English) Zbl 0623.47060 Sib. Math. J. 26, 365-369 (1985). MSC: 47F05 47A10 PDFBibTeX XMLCite \textit{L. S. Koplienko}, Sib. Math. J. 26, 365--369 (1985; Zbl 0623.47060) Full Text: DOI
Skriganov, M. M. The spectrum band structure of the three-dimensional Schrödinger operator with periodic potential. (English) Zbl 0578.47003 Invent. Math. 80, 107-121 (1985). Reviewer: H.Kalf MSC: 47A10 47F05 35J10 PDFBibTeX XMLCite \textit{M. M. Skriganov}, Invent. Math. 80, 107--121 (1985; Zbl 0578.47003) Full Text: DOI EuDML
Popov, V. N.; Skriganov, M. M. Remark on the spectrum structure of the two-dimensional Schrödinger operator with the periodic potential. (English) Zbl 0532.47035 J. Sov. Math. 24, 239-240 (1984). MSC: 47F05 47A10 47Gxx 35J10 35P05 PDFBibTeX XMLCite \textit{V. N. Popov} and \textit{M. M. Skriganov}, J. Sov. Math. 24, 239--240 (1984; Zbl 0532.47035) Full Text: DOI
Knowles, Ian On essential self-adjointness for Schrödinger operators with wildly oscillating potentials. (English) Zbl 0403.47018 J. Math. Anal. Appl. 66, 574-585 (1978). MSC: 47F05 47B25 35J10 PDFBibTeX XMLCite \textit{I. Knowles}, J. Math. Anal. Appl. 66, 574--585 (1978; Zbl 0403.47018) Full Text: DOI
Combescure, M.; Ginibre, J. Spectral and scattering theory for the Schrödinger operator with strongly oscillating potentials. (English) Zbl 0336.47007 Ann. Inst. Henri Poincaré, Nouv. Sér., Sect. A 24, 17-30 (1976). MSC: 47A40 35J10 35P25 PDFBibTeX XMLCite \textit{M. Combescure} and \textit{J. Ginibre}, Ann. Inst. Henri Poincaré, Nouv. Sér., Sect. A 24, 17--30 (1976; Zbl 0336.47007) Full Text: Numdam EuDML