Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians / by Bernard Helffer, Francis Nier
(Lecture Notes in Mathematics ; 1862)
| データ種別 | 電子ブック |
|---|---|
| 出版者 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
| 出版年 | 2005 |
| 本文言語 | 英語 |
| 大きさ | X, 209 p : online resource |
書誌詳細を非表示
| 内容注記 | Kohn's Proof of the Hypoellipticity of the Hörmander Operators Compactness Criteria for the Resolvent of Schrödinger Operators Global Pseudo-differential Calculus Analysis of some Fokker-Planck Operator Return to Equillibrium for the Fokker-Planck Operator Hypoellipticity and Nilpotent Groups Maximal Hypoellipticity for Polynomial of Vector Fields and Spectral Byproducts On Fokker-Planck Operators and Nilpotent Techniques Maximal Microhypoellipticity for Systems and Applications to Witten Laplacians Spectral Properties of the Witten-Laplacians in Connection with Poincaré Inequalities for Laplace Integrals Semi-classical Analysis for the Schrödinger Operator: Harmonic Approximation Decay of Eigenfunctions and Application to the Splitting Semi-classical Analysis and Witten Laplacians: Morse Inequalities Semi-classical Analysis and Witten Laplacians: Tunneling Effects Accurate Asymptotics for the Exponentially Small Eigenvalues of the Witten Laplacian Application to the Fokker-Planck Equation Epilogue Index |
|---|---|
| 一般注記 | 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 |
| 著者標目 | *Helffer, Bernard author Nier, Francis author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Partial differential equations LCSH:Geometry LCSH:Quantum physics LCSH:Statistics LCSH:Thermodynamics LCSH:Heat engineering LCSH:Heat transfer LCSH:Mass transfer FREE:Mathematics FREE:Partial Differential Equations FREE:Engineering Thermodynamics, Heat and Mass Transfer FREE:Geometry FREE:Global Analysis and Analysis on Manifolds FREE:Quantum Physics FREE:Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences |
| 分 類 | DC23:515.353 |
| 巻冊次 | ISBN:9783540315537 
|
| ISBN | 9783540315537 |
| URL | http://dx.doi.org/10.1007/b104762 |
目次／あらすじ