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Counting Function of Characteristic Values and Magnetic Resonances

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBRUNEAU, Vincent
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBONY, Jean-Francois
hal.structure.identifierFacultad de Matemáticas [Santiago de Chile]
dc.contributor.authorRAIKOV, Georgi
dc.date.accessioned2024-04-04T02:18:17Z
dc.date.available2024-04-04T02:18:17Z
dc.date.issued2014
dc.identifier.issn0360-5302
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189297
dc.description.abstractEnWe consider the meromorphic operator-valued function I-K(z)=I-A(z)/z where A is holomorphic on the domain ?< subset of>C, and has values in the class of compact operators acting in a given Hilbert space. Under the assumption that A(0) is a selfadjoint operator which can be of infinite rank, we study the distribution near the origin of the characteristic values of I-K, i.e. the complex numbers w0 for which the operator I-K(w) is not invertible, and we show that generically the characteristic values of I-K converge to 0 with the same rate as the eigenvalues of A(0). We apply our abstract results to the investigation of the resonances of the operator H=H-0+V where H-0 is the shifted 3D Schrodinger operator with constant magnetic field of scalar intensity b>0, and V: (3) is the electric potential which admits a suitable decay at infinity. It is well known that the spectrum sigma(H-0) of H-0 is purely absolutely continuous, coincides with [0, +[, and the so-called Landau levels 2bq with integer q0, play the role of thresholds in sigma(H-0). We study the asymptotic distribution of the resonances near any given Landau level, and under generic assumptions obtain the main asymptotic term of the corresponding resonance counting function, written explicitly in the terms of appropriate Toeplitz operators.
dc.language.isoen
dc.publisherTaylor & Francis
dc.title.enCounting Function of Characteristic Values and Magnetic Resonances
dc.typeArticle de revue
dc.identifier.doi10.1080/03605302.2013.777453
dc.subject.halMathématiques [math]/Théorie spectrale [math.SP]
bordeaux.journalCommunications in Partial Differential Equations
bordeaux.page274-305
bordeaux.volume39
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue2
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00988981
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00988981v1
bordeaux.COinSctx_ver=Z39.88-2004&amp;rft_val_fmt=info:ofi/fmt:kev:mtx:journal&amp;rft.jtitle=Communications%20in%20Partial%20Differential%20Equations&amp;rft.date=2014&amp;rft.volume=39&amp;rft.issue=2&amp;rft.spage=274-305&amp;rft.epage=274-305&amp;rft.eissn=0360-5302&amp;rft.issn=0360-5302&amp;rft.au=BRUNEAU,%20Vincent&amp;BONY,%20Jean-Francois&amp;RAIKOV,%20Georgi&amp;rft.genre=article


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