Overview
- Develops basic vector-bundle-valued objects of geometric analysis from scratch
- Gives a detailed proof of the Feynman-Kac fomula with singular potentials on manifolds
- Includes previously unpublished results
Part of the book series: Operator Theory: Advances and Applications (OT, volume 264)
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Table of contents (14 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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 Since it also includes unpublished findings and new proofs of recently published results, it will also be interesting for researchers from geometric analysis, stochastic analysis, spectral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..
Authors and Affiliations
Bibliographic Information
Book Title: Covariant Schrödinger Semigroups on Riemannian Manifolds
Authors: Batu Güneysu
Series Title: Operator Theory: Advances and Applications
DOI: https://doi.org/10.1007/978-3-319-68903-6
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-68902-9Published: 23 January 2018
Softcover ISBN: 978-3-319-88678-7Published: 06 June 2019
eBook ISBN: 978-3-319-68903-6Published: 22 December 2017
Series ISSN: 0255-0156
Series E-ISSN: 2296-4878
Edition Number: 1
Number of Pages: XVIII, 239
Topics: Global Analysis and Analysis on Manifolds, Partial Differential Equations