Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1862)
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Table of contents (19 chapters)
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Front Matter
Keywords
About this book
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.
Reviews
From the reviews of the first edition:
"The aim of this text is to give an account of how the known techniques from partial differential equations and spectral theory can be applied for the analysis of Fokker-Plank operators or Witten Laplacians … . This synthetic text is very challenging and useful for researchers in partial differential equations, probability theory and mathematical physics." (Viorel Iftimie, Zentralblatt MATH, Vol. 1072, 2005)
Bibliographic Information
Book Title: Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians
Authors: Bernard Helffer, Francis Nier
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/b104762
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2005
Softcover ISBN: 978-3-540-24200-0Published: 11 February 2005
eBook ISBN: 978-3-540-31553-7Published: 17 January 2005
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: X, 209
Topics: Partial Differential Equations, Engineering Thermodynamics, Heat and Mass Transfer, Geometry, Global Analysis and Analysis on Manifolds, Quantum Physics, Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences