02963nam 22005295 450 991034932040332120200706190753.03-030-30545-710.1007/978-3-030-30545-1(CKB)4100000009273655(DE-He213)978-3-030-30545-1(MiAaPQ)EBC5896715(PPN)269145621(EXLCZ)99410000000927365520190911d2019 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierMicrolocal Analysis, Sharp Spectral Asymptotics and Applications IV Magnetic Schrödinger Operator 2 /by Victor Ivrii1st ed. 2019.Cham :Springer International Publishing :Imprint: Springer,2019.1 online resource (XXIII, 714 p. 1 illus.) 3-030-30544-9 Includes bibliographical references and index.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.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.Mathematical analysisAnalysis (Mathematics)Mathematical physicsAnalysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12007Mathematical Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/M35000Mathematical analysis.Analysis (Mathematics).Mathematical physics.Analysis.Mathematical Physics.515Ivrii Victorauthttp://id.loc.gov/vocabulary/relators/aut478877MiAaPQMiAaPQMiAaPQBOOK9910349320403321Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV2510587UNINA