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Math. Phys.", "year": "2008", "url": "https://doi.org/10.1007/s00220-008-0453-1", "author": [ "Rupert L. Frank","Barry Simon","Timo Weidl" ], "authors": [ {"first" : "Rupert L.", "last" : "Frank"}, {"first" : "Barry", "last" : "Simon"}, {"first" : "Timo", "last" : "Weidl"} ], "volume": "282","number": "1","pages": "199--208","abstract": "We prove general comparison theorems for eigenvalues of perturbed Schrödinger operators that allow proof of Lieb\u2013Thirring bounds for suitable non-free Schrödinger operators and Jacobi matrices.", "mrclass" : "35J10 (35P15 47B36 47F05 47N50 81Q15)", "mrreviewer" : "Pavel V. Exner", "mrnumber" : "2415477", "issn" : "0010-3616", "doi" : "10.1007/s00220-008-0453-1", "bibtexKey": "MR2415477" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2d12a32fc0186ec81b846a3d8aeebdad6/mathematik", "tags" : [ "Eigenvalue","IADM","Weidl","asymptotics","from:elkepeter" ], "intraHash" : "d12a32fc0186ec81b846a3d8aeebdad6", "interHash" : "d46758b862531ca22f55be9301846ee3", "label" : "Eigenvalue asymptotics for locally perturbed second-order differential operators", "user" : "mathematik", "description" : "", "date" : "2022-03-30 16:25:09", "changeDate" : "2023-04-21 13:25:45", "count" : 2, "pub-type": "article", "journal": "J. London Math. Soc. (2)", "year": "1999", "url": "https://doi.org/10.1112/S0024610799007024", "author": [ "Timo Weidl" ], "authors": [ {"first" : "Timo", "last" : "Weidl"} ], "volume": "59","number": "1","pages": "227--251","abstract": "We consider the appearance of discrete spectrum in spectral gaps of magnetic Schrödinger operators with electric background field under strong, localised perturbations. We show that for compactly supported perturbations the asymptotics of the counting function of the occurring eigenvalues in the limit of a strong perturbation does not depend on the magnetic field nor on the background field.", "mrclass" : "35P20 (35J10 47F05 47N50 81Q10)", "mrreviewer" : "Günter Berger", "mrnumber" : "1688500", "issn" : "0024-6107", "doi" : "10.1112/S0024610799007024", "bibtexKey": "MR1688500" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2d12a32fc0186ec81b846a3d8aeebdad6/elkepeter", "tags" : [ "Eigenvalue","IADM","Weidl","asymptotics" ], "intraHash" : "d12a32fc0186ec81b846a3d8aeebdad6", "interHash" : "d46758b862531ca22f55be9301846ee3", "label" : "Eigenvalue asymptotics for locally perturbed second-order differential operators", "user" : "elkepeter", "description" : "", "date" : "2022-03-30 16:25:09", "changeDate" : "2023-04-21 13:24:55", "count" : 2, "pub-type": "article", "journal": "J. London Math. Soc. (2)", "year": "1999", "url": "https://doi.org/10.1112/S0024610799007024", "author": [ "Timo Weidl" ], "authors": [ {"first" : "Timo", "last" : "Weidl"} ], "volume": "59","number": "1","pages": "227--251","abstract": "We consider the appearance of discrete spectrum in spectral gaps of magnetic Schrödinger operators with electric background field under strong, localised perturbations. We show that for compactly supported perturbations the asymptotics of the counting function of the occurring eigenvalues in the limit of a strong perturbation does not depend on the magnetic field nor on the background field.", "mrclass" : "35P20 (35J10 47F05 47N50 81Q10)", "mrreviewer" : "Günter Berger", "mrnumber" : "1688500", "issn" : "0024-6107", "doi" : "10.1112/S0024610799007024", "bibtexKey": "MR1688500" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/210c4308b8b87e7bdea79b62aa1516ab9/hermann", "tags" : [ "Laplacian;","bounds}","discrete","eigenvalue","spectrum;","{Magnetic" ], "intraHash" : "10c4308b8b87e7bdea79b62aa1516ab9", "interHash" : "ec89490965296006eb92fd562de5995f", "label" : "Semiclassical bounds in magnetic bottles", "user" : "hermann", "description" : "", "date" : "2017-05-18 11:32:12", "changeDate" : "2017-05-18 09:32:12", "count" : 4, "pub-type": "article", "journal": "REVIEWS IN MATHEMATICAL PHYSICS","publisher":"WORLD SCIENTIFIC PUBL CO PTE LTD","address":"5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE", "year": "{2016}", "url": "", "author": [ "Diana Barseghyan","Pavel Exner","Hynek Kovarik","Timo Weidl" ], "authors": [ {"first" : "Diana", "last" : "Barseghyan"}, {"first" : "Pavel", "last" : "Exner"}, {"first" : "Hynek", "last" : "Kovarik"}, {"first" : "Timo", "last" : "Weidl"} ], "volume": "28","number": "1","abstract": "The aim of the paper is to derive spectral estimates into several\n classes of magnetic systems. They include three-dimensional regions with\n Dirichlet boundary as well as a particle in R-3 confined by a local\n change of the magnetic field. We establish two-dimensional\n Berezin-Li-Yau and Lieb-Thirring-type bounds in the presence of magnetic\n fields and, using them, get three-dimensional estimates for the\n eigenvalue moments of the corresponding magnetic Laplacians.", "author-email" : "dianabar@ujf.cas.cz\n exner@ujf.cas.cz\n hynek.kovarik@unibs.it\n weidl@mathematik.uni-stuttgart.de", "article-number" : "1650002", "issn" : "0129-055X", "researcherid-numbers" : "Kovarik, Hynek/K-9521-2015", "keywords-plus" : "LIEB-THIRRING INEQUALITIES; SCHRODINGER-OPERATORS; ASYMPTOTICS;\n EIGENVALUES; DIRICHLET; BEHAVIOR; DOMAINS", "funding-acknowledgement" : "Czech Science Foundation (GACR) [14-06818S]; University of Ostrava;\n project ``Support of Research in the Moravian-Silesian Region'';\n Gruppo Nazionale per Analisi Matematica, la Probabilita e le loro\n Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica\n (INdAM); MIUR-PRIN; DFG [WE 1964/4-1, GRK 1838]", "research-areas" : "Physics", "orcid-numbers" : "Kovarik, Hynek/0000-0003-3647-8447", "eissn" : "1793-6659", "number-of-cited-references" : "22", "web-of-science-categories" : "Physics, Mathematical", "affiliation" : "Barseghyan, D; Exner, P (Reprint Author), Acad Sci Czech Republic, Inst Nucl Phys, Dept Theoret Phys, CZ-25068 Rez, Czech Republic.\n Barseghyan, D (Reprint Author), Univ Ostrava, Fac Sci, Dept Math, 30 Dubna 22, CZ-70103 Ostrava, Czech Republic.\n Exner, P (Reprint Author), Czech Tech Univ, Doppler Inst Math Phys & Appl Math, Brehova 7, Prague 11519, Czech Republic.\n Kovarik, H (Reprint Author), Univ Brescia, Sez Matemat, Dicatam, Via Branze 38, I-25123 Brescia, Italy.\n Weidl, T (Reprint Author), Univ Stuttgart, Inst Anal Dynam & Modellierung, Fak Math & Phys, Pfaffenwaldring 57, D-70569 Stuttgart, Germany.\n Barseghyan, Diana; Exner, Pavel, Acad Sci Czech Republic, Inst Nucl Phys, Dept Theoret Phys, CZ-25068 Rez, Czech Republic.\n Barseghyan, Diana, Univ Ostrava, Fac Sci, Dept Math, 30 Dubna 22, CZ-70103 Ostrava, Czech Republic.\n Exner, Pavel, Czech Tech Univ, Doppler Inst Math Phys & Appl Math, Brehova 7, Prague 11519, Czech Republic.\n Kovarik, Hynek, Univ Brescia, Sez Matemat, Dicatam, Via Branze 38, I-25123 Brescia, Italy.\n Weidl, Timo, Univ Stuttgart, Inst Anal Dynam & Modellierung, Fak Math & Phys, Pfaffenwaldring 57, D-70569 Stuttgart, Germany.", "funding-text" : "The research was supported by the Czech Science Foundation (GACR) within\n the project 14-06818S. D.B. acknowledges the support of the University\n of Ostrava and the project ``Support of Research in the\n Moravian-Silesian Region 2013''. H.K. was supported by the Gruppo\n Nazionale per Analisi Matematica, la Probabilita e le loro Applicazioni\n (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). The\n support of MIUR-PRIN2010-11 grant for the project ``Calcolo delle\n variazioni'' (H.K.) is also gratefully acknowledged. T.W. was in part\n supported by the DFG project WE 1964/4-1 and the DFG GRK 1838.", "language" : "English", "times-cited" : "0", "doi" : "10.1142/S0129055X16500021", "bibtexKey": "ISI:000372802900002" } ] }