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＜電子ブック＞
Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians / by Francis Nier, Bernard Helffer
(Lecture Notes in Mathematics. ISSN:16179692 ; 1862)

版	1st ed. 2005.
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
著者標目	*Nier, Francis author Helffer, Bernard author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Thermodynamics LCSH:Heat engineering LCSH:Heat transfer LCSH:Mass transfer LCSH:Geometry LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Quantum physics LCSH:Statistics  FREE:Differential Equations FREE:Engineering Thermodynamics, Heat and Mass Transfer FREE:Geometry FREE:Global Analysis and Analysis on Manifolds FREE:Quantum Physics FREE:Statistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/b104762

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