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Hypoelliptic Estimates and Spectral Theory for FokkerPlanck Operators and Witten Laplacians - Lecture Notes in Mathematics
Author: Francis Nier, Bernard Helffer

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 i...  more »s 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.  « less

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ISBN-13: 9783540242000
ISBN-10: 3540242007
Publication Date: 4/6/2005
Pages: 209
Edition: 1
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Publisher: Springer
Book Type: Paperback
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