Filonov, Nikolay; Kachkovskiy, Ilya On spectral bands of discrete periodic operators. (English) Zbl 07798473 Commun. Math. Phys. 405, No. 2, Paper No. 21, 17 p. (2024). MSC: 35J10 39A12 35P99 PDFBibTeX XMLCite \textit{N. Filonov} and \textit{I. Kachkovskiy}, Commun. Math. Phys. 405, No. 2, Paper No. 21, 17 p. (2024; Zbl 07798473) Full Text: DOI arXiv
Dorodnyi, M. High-energy homogenization of a multidimensional nonstationary Schrödinger equation. (English) Zbl 07788013 Russ. J. Math. Phys. 30, No. 4, 480-500 (2023). MSC: 35B27 35B45 35J25 35K15 PDFBibTeX XMLCite \textit{M. Dorodnyi}, Russ. J. Math. Phys. 30, No. 4, 480--500 (2023; Zbl 07788013) Full Text: DOI arXiv
Kerner, Joachim; Täufer, Matthias On the spectral gap of higher-dimensional Schrödinger operators on large domains. (English) Zbl 1522.35528 Asymptotic Anal. 133, No. 1-2, 77-89 (2023). MSC: 35Q99 35P15 35J10 33C10 35B40 PDFBibTeX XMLCite \textit{J. Kerner} and \textit{M. Täufer}, Asymptotic Anal. 133, No. 1--2, 77--89 (2023; Zbl 1522.35528) Full Text: DOI arXiv
Simon, Barry Twelve tales in mathematical physics: an expanded Heineman Prize lecture. (English) Zbl 1507.01028 J. Math. Phys. 63, No. 2, Article ID 021101, 93 p. (2022). MSC: 01A65 81-01 82-01 PDFBibTeX XMLCite \textit{B. Simon}, J. Math. Phys. 63, No. 2, Article ID 021101, 93 p. (2022; Zbl 1507.01028) Full Text: DOI arXiv
Kerner, Joachim Lower bounds on the spectral gap of one-dimensional Schrödinger operators. (English) Zbl 1518.34088 Arch. Math. 119, No. 6, 613-622 (2022). Reviewer: Kadriye Aydemir (Antalya) MSC: 34L15 34L40 47E05 34L05 PDFBibTeX XMLCite \textit{J. Kerner}, Arch. Math. 119, No. 6, 613--622 (2022; Zbl 1518.34088) Full Text: DOI
Liu, Wencai Irreducibility of the Fermi variety for discrete periodic Schrödinger operators and embedded eigenvalues. (English) Zbl 1484.35169 Geom. Funct. Anal. 32, No. 1, 1-30 (2022). MSC: 35J10 14N05 32B15 47A75 14H10 PDFBibTeX XMLCite \textit{W. Liu}, Geom. Funct. Anal. 32, No. 1, 1--30 (2022; Zbl 1484.35169) Full Text: DOI arXiv
Akhmatova, A. R.; Aksenova, E. S.; Sloushch, V. A.; Suslina, T. A. Homogenization of the parabolic equation with periodic coefficients at the edge of a spectral gap. (English) Zbl 1484.35027 Complex Var. Elliptic Equ. 67, No. 3, 523-555 (2022). MSC: 35B27 35B25 35K15 47D06 PDFBibTeX XMLCite \textit{A. R. Akhmatova} et al., Complex Var. Elliptic Equ. 67, No. 3, 523--555 (2022; Zbl 1484.35027) Full Text: DOI
Christiansen, Jacob S.; Simon, Barry; Zinchenko, Maxim Remarks on periodic Jacobi matrices on trees. (English) Zbl 1462.81095 J. Math. Phys. 62, No. 4, Article ID 042101, 7 p. (2021). MSC: 81Q35 47B36 05C05 05C69 05C15 PDFBibTeX XMLCite \textit{J. S. Christiansen} et al., J. Math. Phys. 62, No. 4, Article ID 042101, 7 p. (2021; Zbl 1462.81095) Full Text: DOI arXiv Link
Berkolaiko, Gregory; Kha, Minh Degenerate band edges in periodic quantum graphs. (English) Zbl 1456.81194 Lett. Math. Phys. 110, No. 11, 2965-2982 (2020). MSC: 81Q35 34B45 05C50 34L05 35J05 35P15 81U30 PDFBibTeX XMLCite \textit{G. Berkolaiko} and \textit{M. Kha}, Lett. Math. Phys. 110, No. 11, 2965--2982 (2020; Zbl 1456.81194) Full Text: DOI arXiv
Do, Ngoc; Kuchment, Peter; Sottile, Frank Generic properties of dispersion relations for discrete periodic operators. (English) Zbl 1454.81060 J. Math. Phys. 61, No. 10, 103502, 19 p. (2020). MSC: 81Q05 81U30 14N10 PDFBibTeX XMLCite \textit{N. Do} et al., J. Math. Phys. 61, No. 10, 103502, 19 p. (2020; Zbl 1454.81060) Full Text: DOI arXiv
Lu, Jianfeng; Watson, Alexander B.; Weinstein, Michael I. Dirac operators and domain walls. (English) Zbl 1442.35275 SIAM J. Math. Anal. 52, No. 2, 1115-1145 (2020). Reviewer: Denis Borisov (Ufa) MSC: 35P05 81Q10 81R25 82D20 PDFBibTeX XMLCite \textit{J. Lu} et al., SIAM J. Math. Anal. 52, No. 2, 1115--1145 (2020; Zbl 1442.35275) Full Text: DOI arXiv
Korotyaev, E.; Saburova, N. Spectral estimates for Schrödinger operators on periodic discrete graphs. (English. Russian original) Zbl 1428.35653 St. Petersbg. Math. J. 30, No. 4, 667-698 (2019); translation from Algebra Anal. 30, No. 4, 61-106 (2018). MSC: 35R02 47A10 05C50 35J10 PDFBibTeX XMLCite \textit{E. Korotyaev} and \textit{N. Saburova}, St. Petersbg. Math. J. 30, No. 4, 667--698 (2019; Zbl 1428.35653); translation from Algebra Anal. 30, No. 4, 61--106 (2018) Full Text: DOI arXiv
Suslina, T. A. Spectral approach to homogenization of elliptic operators in a perforated space. (English) Zbl 1411.35029 Rev. Math. Phys. 30, No. 8, Article ID 1840016, 57 p. (2018). Reviewer: Alain Brillard (Riedisheim) MSC: 35B27 47A10 35B40 35J25 PDFBibTeX XMLCite \textit{T. A. Suslina}, Rev. Math. Phys. 30, No. 8, Article ID 1840016, 57 p. (2018; Zbl 1411.35029) Full Text: DOI
Hannabuss, Keith C. T-duality and the bulk-boundary correspondence. (English) Zbl 1388.81540 J. Geom. Phys. 124, 421-435 (2018). MSC: 81T30 82D20 46L05 46L60 PDFBibTeX XMLCite \textit{K. C. Hannabuss}, J. Geom. Phys. 124, 421--435 (2018; Zbl 1388.81540) Full Text: DOI arXiv
Kha, Minh Green’s function asymptotics of periodic elliptic operators on abelian coverings of compact manifolds. (English) Zbl 1382.35172 J. Funct. Anal. 274, No. 2, 341-387 (2018). Reviewer: James Bernard Kennedy (Lisboa) MSC: 35P05 58J37 35J08 35J10 35J15 58J05 58J50 PDFBibTeX XMLCite \textit{M. Kha}, J. Funct. Anal. 274, No. 2, 341--387 (2018; Zbl 1382.35172) 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
Cornean, Horia D.; Helffer, Bernard; Purice, Radu Low lying spectral gaps induced by slowly varying magnetic fields. (English) Zbl 1372.35255 J. Funct. Anal. 273, No. 1, 206-282 (2017). Reviewer: Boris A. Malomed (Tel Aviv) MSC: 35Q40 81Q10 78A60 PDFBibTeX XMLCite \textit{H. D. Cornean} et al., J. Funct. Anal. 273, No. 1, 206--282 (2017; Zbl 1372.35255) Full Text: DOI arXiv
Zelenko, Leonid Virtual bound levels in a gap of the essential spectrum of the weakly perturbed periodic Schrödinger operator. (English) Zbl 1422.47051 Integral Equations Oper. Theory 85, No. 3, 307-345 (2016). Reviewer: Michael Perelmuter (Kyïv) MSC: 47F05 47A75 35P05 35P20 47A55 81Q10 81Q15 PDFBibTeX XMLCite \textit{L. Zelenko}, Integral Equations Oper. Theory 85, No. 3, 307--345 (2016; Zbl 1422.47051) Full Text: DOI
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
Raikov, Georgi Spectral asymptotics for waveguides with perturbed periodic twisting. (English) Zbl 1337.35105 J. Spectr. Theory 6, No. 2, 331-372 (2016). MSC: 35P20 81Q10 35J10 PDFBibTeX XMLCite \textit{G. Raikov}, J. Spectr. Theory 6, No. 2, 331--372 (2016; Zbl 1337.35105) Full Text: DOI arXiv
Borisov, Denis; Hoecker-Escuti, Francisco; Veselić, Ivan Expansion of the almost sure spectrum in the weak disorder regime. (English) Zbl 1331.82026 J. Funct. Anal. 270, No. 5, 1684-1718 (2016). MSC: 82B44 PDFBibTeX XMLCite \textit{D. Borisov} et al., J. Funct. Anal. 270, No. 5, 1684--1718 (2016; Zbl 1331.82026) Full Text: DOI arXiv
Boumaza, Hakim; Najar, Hatem Lifshitz tails for continuous matrix-valued Anderson models. (English) Zbl 1360.82039 J. Stat. Phys. 160, No. 2, 371-396 (2015). MSC: 82B44 47B80 PDFBibTeX XMLCite \textit{H. Boumaza} and \textit{H. Najar}, J. Stat. Phys. 160, No. 2, 371--396 (2015; Zbl 1360.82039) Full Text: DOI arXiv
Shen, Zhongwei Lifshitz tails for Anderson models with sign-indefinite single-site potentials. (English) Zbl 1372.47050 Math. Nachr. 288, No. 13, 1538-1563 (2015). Reviewer: Constanza Rojas-Molina (Bonn) MSC: 47B80 47N50 35P20 PDFBibTeX XMLCite \textit{Z. Shen}, Math. Nachr. 288, No. 13, 1538--1563 (2015; Zbl 1372.47050) Full Text: DOI arXiv
Korotyaev, Evgeny; Saburova, Natalia Schrödinger operators on periodic discrete graphs. (English) Zbl 1297.47050 J. Math. Anal. Appl. 420, No. 1, 576-611 (2014). Reviewer: Michael Perelmuter (Kyïv) MSC: 47E05 34B45 34L05 34L40 81Q10 PDFBibTeX XMLCite \textit{E. Korotyaev} and \textit{N. Saburova}, J. Math. Anal. Appl. 420, No. 1, 576--611 (2014; Zbl 1297.47050) Full Text: DOI arXiv
Borisov, Denis; Veselić, Ivan Spectral gaps for self-adjoint second order operators. (English) Zbl 1275.47098 Z. Anal. Anwend. 31, No. 4, 473-505 (2012). Reviewer: Petar Popivanov (Sofia) MSC: 47F05 35P15 35J15 PDFBibTeX XMLCite \textit{D. Borisov} and \textit{I. Veselić}, Z. Anal. Anwend. 31, No. 4, 473--505 (2012; Zbl 1275.47098) 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
Briet, Philippe; Cornean, Horia D.; Savoie, Baptiste A rigorous proof of the Landau-Peierls formula and much more. (English) Zbl 1251.82006 Ann. Henri Poincaré 13, No. 1, 1-40 (2012). Reviewer: Giovanni Mascali (Arcavacata di Rende) MSC: 82B10 82D35 82D37 81Q10 81Q15 81V99 PDFBibTeX XMLCite \textit{P. Briet} et al., Ann. Henri Poincaré 13, No. 1, 1--40 (2012; Zbl 1251.82006) Full Text: DOI arXiv
Chen, Duo-Yuan; Huang, Min-Jei On the semiclassical approximation to the eigenvalue gap of Schrödinger operators. (English) Zbl 1242.34151 J. Math. Anal. Appl. 389, No. 2, 1251-1258 (2012). Reviewer: Mihai Pascu (Bucureşti) MSC: 34L40 34L15 34L20 PDFBibTeX XMLCite \textit{D.-Y. Chen} and \textit{M.-J. Huang}, J. Math. Anal. Appl. 389, No. 2, 1251--1258 (2012; Zbl 1242.34151) Full Text: DOI
Lenz, Daniel; Stollmann, Peter; Veselić, Ivan Generalized eigenfunctions and spectral theory for strongly local Dirichlet forms. (English) Zbl 1248.35133 Janas, Jan (ed.) et al., Spectral theory and analysis. Conference on operator theory, analysis and mathematical physics (OTAMP) 2008, Bedlewo, Poland. Berlin: Springer (ISBN 978-3-7643-9993-1/hbk; 978-94-007-0431-2/ebook). Operator Theory: Advances and Applications 214, 83-106 (2011). Reviewer: Michael Perelmuter (Kyïv) MSC: 35P05 81Q10 PDFBibTeX XMLCite \textit{D. Lenz} et al., Oper. Theory: Adv. Appl. 214, 83--106 (2011; Zbl 1248.35133) Full Text: DOI arXiv
Klopp, Frédéric; Metzger, Bernd The Gross-Pitaevskii functional with a random background potential and condensation in the single particle ground state. (English) Zbl 1242.82011 Math. Phys. Anal. Geom. 14, No. 4, 321-341 (2011). MSC: 82B20 82B44 60H25 PDFBibTeX XMLCite \textit{F. Klopp} and \textit{B. Metzger}, Math. Phys. Anal. Geom. 14, No. 4, 321--341 (2011; Zbl 1242.82011) Full Text: DOI arXiv
Bunoiu, R.; Cardone, G.; Suslina, T. Spectral approach to homogenization of an elliptic operator periodic in some directions. (English) Zbl 1221.35256 Math. Methods Appl. Sci. 34, No. 9, 1075-1096 (2011). Reviewer: Petru A. Cojuhari (Kraków) MSC: 35P05 35B27 35J15 47F05 35B05 PDFBibTeX XMLCite \textit{R. Bunoiu} et al., Math. Methods Appl. Sci. 34, No. 9, 1075--1096 (2011; Zbl 1221.35256) Full Text: DOI arXiv
Ghribi, Fatma; Klopp, Frédéric Localization for the random displacement model at weak disorder. (English) Zbl 1210.82063 Ann. Henri Poincaré 11, No. 1-2, 127-149 (2010). MSC: 82D30 PDFBibTeX XMLCite \textit{F. Ghribi} and \textit{F. Klopp}, Ann. Henri Poincaré 11, No. 1--2, 127--149 (2010; Zbl 1210.82063) Full Text: DOI arXiv
Kirsch, Werner; Veselić, Ivan Lifshitz tails for a class of Schrödinger operators with random breather-type potential. (English) Zbl 1198.35064 Lett. Math. Phys. 94, No. 1, 27-39 (2010). MSC: 35J10 82B44 60H25 PDFBibTeX XMLCite \textit{W. Kirsch} and \textit{I. Veselić}, Lett. Math. Phys. 94, No. 1, 27--39 (2010; Zbl 1198.35064) Full Text: DOI arXiv
Klopp, Frédéric; Nakamura, Shu Spectral extrema and Lifshitz tails for non-monotonous alloy type models. (English) Zbl 1198.35065 Commun. Math. Phys. 287, No. 3, 1133-1143 (2009). MSC: 35J10 81Q10 35R60 60H25 PDFBibTeX XMLCite \textit{F. Klopp} and \textit{S. Nakamura}, Commun. Math. Phys. 287, No. 3, 1133--1143 (2009; Zbl 1198.35065) Full Text: DOI arXiv
Briet, Philippe; Kovařík, Hynek; Raikov, Georgi; Soccorsi, Eric Eigenvalue asymptotics in a twisted waveguide. (English) Zbl 1195.35119 Commun. Partial Differ. Equations 34, No. 8, 818-836 (2009). Reviewer: Michael Perelmuter (Kyïv) MSC: 35J10 81Q10 35P20 PDFBibTeX XMLCite \textit{P. Briet} et al., Commun. Partial Differ. Equations 34, No. 8, 818--836 (2009; Zbl 1195.35119) Full Text: DOI arXiv Link
Hou, Songbo Critical potentials of the eigenvalue ratios of Schrödinger operators. (English) Zbl 1156.58307 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 1, 524-528 (2009). MSC: 58J50 49R50 35P99 PDFBibTeX XMLCite \textit{S. Hou}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 1, 524--528 (2009; Zbl 1156.58307) Full Text: DOI
Frank, Rupert L.; Simon, Barry; Weidl, Timo Eigenvalue bounds for perturbations of Schrödinger operators and Jacobi matrices with regular ground states. (English) Zbl 1158.35021 Commun. Math. Phys. 282, No. 1, 199-208 (2008). MSC: 35J10 81Q15 35P15 47B36 47N50 35B05 PDFBibTeX XMLCite \textit{R. L. Frank} et al., Commun. Math. Phys. 282, No. 1, 199--208 (2008; Zbl 1158.35021) Full Text: DOI arXiv Link
Hundertmark, Dirk; Simon, Barry Eigenvalue bounds in the gaps of Schrödinger operators and Jacobi matrices. (English) Zbl 1135.47026 J. Math. Anal. Appl. 340, No. 2, 892-900 (2008). Reviewer: Leonid Golinskii (Kharkov) MSC: 47B36 47A55 PDFBibTeX XMLCite \textit{D. Hundertmark} and \textit{B. Simon}, J. Math. Anal. Appl. 340, No. 2, 892--900 (2008; Zbl 1135.47026) Full Text: DOI arXiv Link
Kuchment, Peter; Pinchover, Yehuda Liouville theorems and spectral edge behavior on Abelian coverings of compact manifolds. (English) Zbl 1127.58015 Trans. Am. Math. Soc. 359, No. 12, 5777-5815 (2007). MSC: 58J05 35B05 32Q99 35J15 35P05 32M99 58J50 PDFBibTeX XMLCite \textit{P. Kuchment} and \textit{Y. Pinchover}, Trans. Am. Math. Soc. 359, No. 12, 5777--5815 (2007; Zbl 1127.58015) Full Text: DOI arXiv
Kondej, Sylwia; Veselić, Ivan Spectral gap of segments of periodic waveguides. (English) Zbl 1110.81320 Lett. Math. Phys. 79, No. 1, 95-98 (2007). MSC: 81Q10 35P15 35J20 35J25 47F05 PDFBibTeX XMLCite \textit{S. Kondej} and \textit{I. Veselić}, Lett. Math. Phys. 79, No. 1, 95--98 (2007; Zbl 1110.81320) Full Text: DOI arXiv
Klopp, Frédéric; Raikov, Georgi Lifshitz tails in constant magnetic fields. (English) Zbl 1188.82028 Commun. Math. Phys. 267, No. 3, 669-701 (2006). MSC: 82B44 81Q10 47N50 47B80 47F05 PDFBibTeX XMLCite \textit{F. Klopp} and \textit{G. Raikov}, Commun. Math. Phys. 267, No. 3, 669--701 (2006; Zbl 1188.82028) Full Text: DOI arXiv Link
Kotani, Motoko; Sunada, Toshikazu Large deviation and the tangent cone at infinity of a crystal lattice. (English) Zbl 1124.60027 Math. Z. 254, No. 4, 837-870 (2006). MSC: 60F10 60G50 58J35 53C21 39A12 PDFBibTeX XMLCite \textit{M. Kotani} and \textit{T. Sunada}, Math. Z. 254, No. 4, 837--870 (2006; Zbl 1124.60027) Full Text: DOI
Matsui, Taku BEC of free bosons on networks. (English) Zbl 1093.82003 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 9, No. 1, 1-26 (2006). Reviewer: Utkir Rozikov (Tashkent) MSC: 82B10 PDFBibTeX XMLCite \textit{T. Matsui}, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 9, No. 1, 1--26 (2006; Zbl 1093.82003) Full Text: DOI arXiv
Kirsch, Werner; Warzel, Simone Anderson localization and Lifshits tails for random surface potentials. (English) Zbl 1127.82033 J. Funct. Anal. 230, No. 1, 222-250 (2006). Reviewer: Johannes F. Brasche (Clausthal) MSC: 82B44 35J10 35P20 35R60 47B80 47N55 60H25 PDFBibTeX XMLCite \textit{W. Kirsch} and \textit{S. Warzel}, J. Funct. Anal. 230, No. 1, 222--250 (2006; Zbl 1127.82033) Full Text: DOI arXiv
El Soufi, Ahmad; Moukadem, Nazih Critical potentials of the eigenvalues and eigenvalue gaps of Schrödinger operators. (English) Zbl 1081.58022 J. Math. Anal. Appl. 314, No. 1, 195-209 (2006). MSC: 58J50 35P15 58E05 PDFBibTeX XMLCite \textit{A. El Soufi} and \textit{N. Moukadem}, J. Math. Anal. Appl. 314, No. 1, 195--209 (2006; Zbl 1081.58022) Full Text: DOI arXiv
Kirsch, Werner; Warzel, Simone Lifshits tails caused by anisotropic decay: the emergence of a quantum-classical regime. (English) Zbl 1093.82011 Math. Phys. Anal. Geom. 8, No. 3, 257-285 (2005). Reviewer: Vicenţiu D. Rădulescu (Craiova) MSC: 82B44 35J10 81Q05 PDFBibTeX XMLCite \textit{W. Kirsch} and \textit{S. Warzel}, Math. Phys. Anal. Geom. 8, No. 3, 257--285 (2005; Zbl 1093.82011) Full Text: DOI arXiv
Birman, M. Sh.; Suslina, T. A. Second order periodic differential operators. Threshold properties and homogenization. (English. Russian original) Zbl 1072.47042 St. Petersbg. Math. J. 15, No. 5, 639-714 (2004); translation from Algebra Anal. 15, No. 5, 1-108 (2003). Reviewer: Anatoly N. Kochubei (Kyïv) MSC: 47F05 35B27 35P99 35J99 PDFBibTeX XMLCite \textit{M. Sh. Birman} and \textit{T. A. Suslina}, St. Petersbg. Math. J. 15, No. 5, 639--714 (2004; Zbl 1072.47042); translation from Algebra Anal. 15, No. 5, 1--108 (2003) Full Text: DOI
Najar, Hatem Lifshitz tails for random acoustic operators. (English) Zbl 1062.35052 J. Math. Phys. 44, No. 4, 1842-1867 (2003). MSC: 35P20 35R60 47B80 60H25 82B44 PDFBibTeX XMLCite \textit{H. Najar}, J. Math. Phys. 44, No. 4, 1842--1867 (2003; Zbl 1062.35052) Full Text: DOI
Helffer, B.; Hoffmann-Ostenhof, T. Spectral theory for periodic Schrödinger operators with reflection symmetries. (English) Zbl 1050.35056 Commun. Math. Phys. 242, No. 3, 501-529 (2003). Reviewer: Michael Perelmuter (Kyïv) MSC: 35P05 35J10 81Q10 PDFBibTeX XMLCite \textit{B. Helffer} and \textit{T. Hoffmann-Ostenhof}, Commun. Math. Phys. 242, No. 3, 501--529 (2003; Zbl 1050.35056) Full Text: DOI
Klopp, Frédéric A remark about internal Lifshitz asymptotes. (Une remarque à propos des asymptotiques de Lifshitz internes.) (French. Abridged English version) Zbl 1003.60063 C. R., Math., Acad. Sci. Paris 335, No. 1, 87-92 (2002). Reviewer: Anatoly N.Kochubei (Kyïv) MSC: 60H25 82B44 47B80 PDFBibTeX XMLCite \textit{F. Klopp}, C. R., Math., Acad. Sci. Paris 335, No. 1, 87--92 (2002; Zbl 1003.60063) Full Text: DOI
Davis, Burgess On the spectral gap for fixed membranes. (English) Zbl 1021.35040 Ark. Mat. 39, No. 1, 65-74 (2001). Reviewer: Lubomira Softova (Bari) MSC: 35K05 35J10 60J65 PDFBibTeX XMLCite \textit{B. Davis}, Ark. Mat. 39, No. 1, 65--74 (2001; Zbl 1021.35040) Full Text: DOI
Aida, Shigeki An estimate of the gap of spectrum of Schrödinger operators which generate hyperbounded semigroups. (English) Zbl 1038.60077 J. Funct. Anal. 185, No. 2, 474-526 (2001). Reviewer: Michael Röckner (Bielefeld) MSC: 60J60 47D07 35J10 35P15 PDFBibTeX XMLCite \textit{S. Aida}, J. Funct. Anal. 185, No. 2, 474--526 (2001; Zbl 1038.60077) Full Text: DOI Link
Kuchment, Peter; Pinchover, Yehuda Integral representations and Liouville theorems for solutions of periodic elliptic equations. (English) Zbl 0986.35028 J. Funct. Anal. 181, No. 2, 402-446 (2001). Reviewer: Shigeru Sakaguchi (Ehime) MSC: 35J15 35C15 35B05 PDFBibTeX XMLCite \textit{P. Kuchment} and \textit{Y. Pinchover}, J. Funct. Anal. 181, No. 2, 402--446 (2001; Zbl 0986.35028) Full Text: DOI arXiv
Weidl, Timo Remarks on virtual bound states for semi-bounded operators. (English) Zbl 0926.47009 Commun. Partial Differ. Equations 24, No. 1-2, 25-60 (1999). MSC: 47A55 47A10 47F05 PDFBibTeX XMLCite \textit{T. Weidl}, Commun. Partial Differ. Equations 24, No. 1--2, 25--60 (1999; Zbl 0926.47009) Full Text: DOI
Karaa, Samir Extremal eigenvalue gaps for the Schrödinger operator with Dirichlet boundary conditions. (English) Zbl 1042.35601 J. Math. Phys. 39, No. 4, 2325-2332 (1998). MSC: 35P15 35J10 PDFBibTeX XMLCite \textit{S. Karaa}, J. Math. Phys. 39, No. 4, 2325--2332 (1998; Zbl 1042.35601) Full Text: DOI
Aida, Shigeki Uniform positivity improving property, Sobolev inequalities, and spectral gaps. (English) Zbl 0914.47041 J. Funct. Anal. 158, No. 1, 152-185 (1998). Reviewer: Piotr Garbaczewski (Zielona Gora) MSC: 47D07 60E15 46G12 PDFBibTeX XMLCite \textit{S. Aida}, J. Funct. Anal. 158, No. 1, 152--185 (1998; Zbl 0914.47041) Full Text: DOI
Jensen, Arne; Nakamura, Shu The 2D Schrödinger equation for a neutral pair in a constant magnetic field. (English) Zbl 0888.47052 Ann. Inst. Henri Poincaré, Phys. Théor. 67, No. 4, 387-410 (1997). MSC: 47N50 81Q10 81U05 PDFBibTeX XMLCite \textit{A. Jensen} and \textit{S. Nakamura}, Ann. Inst. Henri Poincaré, Phys. Théor. 67, No. 4, 387--410 (1997; Zbl 0888.47052) Full Text: Numdam EuDML
Klopp, Frédéric Localization for some continuous random Schrödinger operators. (English) Zbl 0820.60044 Commun. Math. Phys. 167, No. 3, 553-569 (1995). MSC: 60H25 82B44 47B80 47N50 81Q10 PDFBibTeX XMLCite \textit{F. Klopp}, Commun. Math. Phys. 167, No. 3, 553--569 (1995; Zbl 0820.60044) Full Text: DOI
Brown, Russell M.; Hislop, P. D.; Martinez, A. Lower bounds on the interaction between cavities connected by a thin tube. (English) Zbl 0802.35109 Duke Math. J. 73, No. 1, 163-176 (1994). Reviewer: S.Jimbo (Sapporo) MSC: 35P15 35J05 PDFBibTeX XMLCite \textit{R. M. Brown} et al., Duke Math. J. 73, No. 1, 163--176 (1994; Zbl 0802.35109) Full Text: DOI
Helffer, Bernard Universal estimate of the gap for the Kac operator in the convex case. (English) Zbl 0802.35110 Commun. Math. Phys. 161, No. 3, 631-643 (1994). Reviewer: S.Jimbo (Sapporo) MSC: 35P15 35Q40 81Q10 PDFBibTeX XMLCite \textit{B. Helffer}, Commun. Math. Phys. 161, No. 3, 631--643 (1994; Zbl 0802.35110) Full Text: DOI
Kirsch, W.; Simon, B. Universal lower bounds on eigenvalue splittings for one dimensional Schrödinger operators. (English) Zbl 0579.34014 Commun. Math. Phys. 97, No. 3, 453-460 (1985). MSC: 34L99 47E05 81Q99 PDFBibTeX XMLCite \textit{W. Kirsch} and \textit{B. Simon}, Commun. Math. Phys. 97, No. 3, 453--460 (1985; Zbl 0579.34014) Full Text: DOI