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Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians

  • Authors
  • Bernard Helffer
  • Francis Nier

Part of the Lecture Notes in Mathematics book series (LNM, volume 1862)

Table of contents

  1. Front Matter
    Pages I-X
  2. Bernard Helffer, Francis Nier
    Pages 1-9
  3. Bernard Helffer, Francis Nier
    Pages 27-42
  4. Bernard Helffer, Francis Nier
    Pages 43-64
  5. Bernard Helffer, Francis Nier
    Pages 65-72
  6. Bernard Helffer, Francis Nier
    Pages 73-78
  7. Bernard Helffer, Francis Nier
    Pages 89-95
  8. Bernard Helffer, Francis Nier
    Pages 147-161
  9. Bernard Helffer, Francis Nier
    Pages 163-172
  10. Bernard Helffer, Francis Nier
    Pages 173-180
  11. Bernard Helffer, Francis Nier
    Pages 189-191
  12. Bernard Helffer, Francis Nier
    Pages 193-193
  13. Bernard Helffer, Francis Nier
    Pages 195-209
  14. Back Matter
    Pages 211-215

About this book

Introduction

There has recently been a renewal of interest in Fokker-Planck operators, motivated by problems in statistical physics, in kinetic equations and differential geometry. Compared to more standard problems in the spectral theory of partial differential operators, those operators are not self-adjoint and only hypoelliptic. The aim of the analysis is to give, as generally as possible, an accurate qualitative and quantitative description of the exponential return to the thermodynamical equilibrium. While exploring and improving recent results in this direction this volume proposes a review of known techniques on: the hypoellipticity of polynomial of vector fields and its global counterpart; the global Weyl-Hörmander pseudo-differential calculus, the spectral theory of non-self-adjoint operators, the semi-classical analysis of Schrödinger-type operators, the Witten complexes and the Morse inequalities.

Keywords

Eigenvalue Fokker-Planck operators Hypoellipticity Maximum Witten Laplacians calculus compactness compactness criteria return to equilibrium

Bibliographic information

  • DOI https://doi.org/10.1007/b104762
  • Copyright Information Springer-Verlag Berlin Heidelberg 2005
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-24200-0
  • Online ISBN 978-3-540-31553-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site