Operator Theory: Advances and Applications

Covariant Schrödinger Semigroups on Riemannian Manifolds

Authors: Güneysu, Batu

  • 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  • Includes previously unpublished results
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eBook $89.00
price for USA in USD (gross)
  • ISBN 978-3-319-68903-6
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  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
  • ISBN 978-3-319-68902-9
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  • Usually dispatched within 3 to 5 business days.
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 Since it also includes unpublished findings and new proofs of recently published results, it will also be interesting for researchers from geometric analysis, stochastic analysis, spectral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..

Table of contents (14 chapters)

  • Sobolev Spaces on Vector Bundles

    Güneysu, Batu

    Pages 1-19

  • Smooth Heat Kernels on Vector Bundles

    Güneysu, Batu

    Pages 21-26

  • Basic Differential Operators in Riemannian Manifolds

    Güneysu, Batu

    Pages 27-48

  • Some Specific Results for the Minimal Heat Kernel

    Güneysu, Batu

    Pages 49-70

  • Wiener Measure and Brownian Motion on Riemannian Manifolds

    Güneysu, Batu

    Pages 71-84

Buy this book

eBook $89.00
price for USA in USD (gross)
  • ISBN 978-3-319-68903-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
  • ISBN 978-3-319-68902-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Covariant Schrödinger Semigroups on Riemannian Manifolds
Authors
Series Title
Operator Theory: Advances and Applications
Series Volume
264
Copyright
2017
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-68903-6
DOI
10.1007/978-3-319-68903-6
Hardcover ISBN
978-3-319-68902-9
Series ISSN
0255-0156
Edition Number
1
Number of Pages
XVIII, 239
Topics