
Francis Nier,Bernard Helffer

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Author: Francis Nier,Bernard Helffer
Publisher: Springer Science & Business Media
ISBN: 9783540242000
Category: Mathematics
Page: 209
View: 5557
There has recently been a renewal of interest in FokkerPlanck 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 selfadjoint 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 WeylHörmander pseudodifferential calculus, the spectral theory of nonselfadjoint operators, the semiclassical analysis of Schrödingertype operators, the Witten complexes, and the Morse inequalities.