Covariant Schrödinger semigroups on Riemannian manifolds / by Batu Güneysu.

Format:

Book

Author/Creator:

Güneysu., Author.

Contributor:

Batu.

Series:

Operator Theory: Advances and Applications, 0255-0156 ; 264

Language:

English

Subjects (All):

Global analysis (Mathematics).

Manifolds (Mathematics).

Differential equations, Partial.

Global Analysis and Analysis on Manifolds.

Partial Differential Equations.

Local Subjects:

Global Analysis and Analysis on Manifolds.

Partial Differential Equations.

Physical Description:

1 online resource (XVIII, 239 p.)

Edition:

1版. 2017.

Place of Publication:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2017.

Summary:

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 Since it also includes unpublished findings and new proofs of recently published results, it will also be interesting for researchers from geometric analysis, stochastic analysis, spectral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 physics.

Contents:

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

Applications.

Notes:

Includes bibliographical references and index.

ISBN:

3-319-68903-7