The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger operator, miscellaneous problems, and multiparticle quantum theory.
In this volume the methods developed in Volumes I, II and III are applied to the Schrödinger and Dirac operators in non-smooth settings and in higher dimensions.
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Inhoudsopgave
Non-smooth theory and higher dimensions.- Irregular coefficients in dimensions 2, 3.- Full-rank case.- Non-full-rank case.- 4D-Schrödinger with degenerating magnetic field.- 4D-Schrödinger Operator with the strong magnetic field.- Eigenvalue asymptotics for Schrödinger and dirac operators with the strong magnetic field.- Eigenvalue asymptotics: 2D case.- Eigenvalue asymptotics: 3D case.Over de auteur
VICTOR IVRII is a professor of mathematics at the University of Toronto. His areas of specialization are analysis, microlocal analysis, spectral theory, partial differential equations and applications to mathematical physics. He proved the Weyl conjecture in 1979, and together with Israel M. Sigal he justified the Scott correction term for heavy atoms and molecules in 1992. He is a Fellow of the Royal Society of Canada (since 1998) and of American Mathematical Society (since 2012).
Taal Engels ● Formaat PDF ● Pagina’s 714 ● ISBN 9783030305451 ● Bestandsgrootte 8.6 MB ● Uitgeverij Springer International Publishing ● Stad Cham ● Land CH ● Gepubliceerd 2019 ● Downloadbare 24 maanden ● Valuta EUR ● ID 7173283 ● Kopieerbeveiliging Sociale DRM
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