02803nmm a2200457 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100001800139245015600157250001700313260006300330300003000393505030100423653002000724653002100744653004600765653001900811653001800830653001700848653003500865653002000900653005500920653001300975653002800988653001801016653003501034653001301069653003401082653008801116700003101204710003401235041001901269989003601288490003301324856006201357082001201419520091401431EB000374862EBX0100000000000000022791400000000000000.0cr|||||||||||||||||||||130626 ||| eng a97835403155371 aNier, Francis00aHypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten LaplacianshElektronische Ressourcecby Francis Nier, Bernard Helffer a1st ed. 2005 aBerlin, HeidelbergbSpringer Berlin Heidelbergc2005, 2005 aX, 209 pbonline resource0 aHarmonic 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 Witte aQuantum Physics aHeat engineering aGlobal Analysis and Analysis on Manifolds aThermodynamics aHeat transfer aStatistics aPartial Differential Equations aQuantum physics aEngineering Thermodynamics, Heat and Mass Transfer aGeometry aManifolds (Mathematics) aMass transfer aPartial differential equations aGeometry aGlobal analysis (Mathematics) aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences1 aHelffer, Bernarde[author]2 aSpringerLink (Online service)07aeng2ISO 639-2 bSpringeraSpringer eBooks 2005-0 aLecture Notes in Mathematics uhttps://doi.org/10.1007/b104762?nosfx=yxVerlag3Volltext0 a515.353 aThere 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