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020 _a9783540315537
_9978-3-540-31553-7
024 7 _a10.1007/b104762
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
072 7 _aPBKJ
_2thema
082 0 4 _a515.353
_223
100 1 _aHelffer, Bernard.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aHypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians
_h[electronic resource] /
_cby Bernard Helffer, Francis Nier.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2005.
300 _aX, 209 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1862
505 0 _aKohn'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.
520 _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.
650 0 _aDifferential equations, partial.
650 0 _aEngineering.
650 0 _aGeometry.
650 0 _aGlobal analysis.
650 0 _aQuantum theory.
650 0 _aStatistics.
650 1 4 _aPartial Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12155
650 2 4 _aEngineering Thermodynamics, Heat and Mass Transfer.
_0http://scigraph.springernature.com/things/product-market-codes/T14000
650 2 4 _aGeometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21006
650 2 4 _aGlobal Analysis and Analysis on Manifolds.
_0http://scigraph.springernature.com/things/product-market-codes/M12082
650 2 4 _aQuantum Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19080
650 2 4 _aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences.
_0http://scigraph.springernature.com/things/product-market-codes/S17020
700 1 _aNier, Francis.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540806424
776 0 8 _iPrinted edition:
_z9783540242000
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1862
856 4 0 _uhttps://doi.org/10.1007/b104762
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c11011
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