Covariant Schrödinger Semigroups on Riemannian Manifolds / by Batu Güneysu

By:

Güneysu, Batu, 1982- [aut]

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Operator Theory: Advances and Applications ; 264 | SpringerLink BücherPublisher: Cham : Birkhäuser, 2017Description: Online-Ressource (XVIII, 239 p, online resource)ISBN:

9783319689036

Subject(s):

Additional physical formats: 9783319689029 | Erscheint auch als: Covariant Schrödinger semigroups on Riemannian manifolds. Druck-Ausgabe Cham : Birkhäuser, 2017. xviii, 239 SeitenMSC: MSC: *47D08 | 58-01 | 58B25 | 58D07 | 58J60 | 53C21RVK: RVK: SK 620LOC classification:

QA614-614.97

DOI: DOI: 10.1007/978-3-319-68903-6Online resources:

Summary: Sobolev spaces on vector bundles -- Smooth heat kernels on vector bundles -- Basis differential operators on Riemannian manifolds -- Some specific results for the minimal heat kernel -- Wiener measure and Brownian motion on Riemannian manifolds -- Contractive Dynkin potentials and Kato potentials -- Foundations of covariant Schrödinger semigroups -- Compactness of resolvents for covariant Schrödinger operators -- L^p properties of covariant Schrödinger semigroups -- Continuity properties of covariant Schrödinger semigroups -- Integral kernels for covariant Schrödinger semigroup -- Essential self-adjointness of covariant Schrödinger semigroups -- Form cores -- ApplicationsSummary: This monograph discusses covariant Schrödinger operators and their heat semigroups on noncompact Riemannian manifolds and aims to fill a gap in the literature, given the fact that the existing literature on Schrödinger operators has mainly focused on scalar Schrödinger operators on Euclidean spaces so far. In particular, the book studies operators that act on sections of vector bundles. In addition, these operators are allowed to have unbounded potential terms, possibly with strong local singularities. The results presented here provide the first systematic study of such operators that is sufficiently general to simultaneously treat the natural operators from quantum mechanics, such as magnetic Schrödinger operators with singular electric potentials, and those from geometry, such as squares of Dirac operators that have smooth but endomorphism-valued and possibly unbounded potentials. The book is largely self-contained, making it accessible for graduate and postgraduate students alike. Since it also includes unpublished findings and new proofs of recently published results, it will also be interesting for researchers from geometric analysis, stochastic analysis, spectral theory, and mathematical physicsPPN: PPN: 1658619609Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA

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