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-H rmander pseudo-differential calculus, the spectral theory of non-self-adjoint operators, the semi-classical analysis of Schr dinger-type operators, the Witten complexes, and the Morse inequalities.
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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-H rmander pseudo-differential calculus, the spectral theory of non-self-adjoint operators, the semi-classical analysis of Schr dinger-type operators, the Witten complexes, and the Morse inequalities.
Imprint | Springer-Verlag |
Country of origin | Germany |
Series | Lecture Notes in Mathematics, 1862 |
Release date | February 2005 |
Availability | Expected to ship within 10 - 15 working days |
First published | 2005 |
Authors | Francis Nier, Bernard Helffer |
Dimensions | 235 x 155 x 16mm (L x W x T) |
Format | Paperback |
Pages | 209 |
Edition | 2005 ed. |
ISBN-13 | 978-3-540-24200-0 |
Barcode | 9783540242000 |
Categories | |
LSN | 3-540-24200-7 |