LEADER 04132nam 2200661 450 001 996466484303316 005 20210218003520.0 010 $a3-540-31553-5 024 7 $a10.1007/b104762 035 $a(CKB)1000000000231894 035 $a(DE-He213)978-3-540-31553-7 035 $a(SSID)ssj0000318185 035 $a(PQKBManifestationID)11267557 035 $a(PQKBTitleCode)TC0000318185 035 $a(PQKBWorkID)10308914 035 $a(PQKB)11074010 035 $a(MiAaPQ)EBC4976178 035 $a(MiAaPQ)EBC5577310 035 $a(MiAaPQ)EBC6352835 035 $a(Au-PeEL)EBL4976178 035 $a(CaONFJC)MIL140211 035 $a(OCoLC)1024263364 035 $a(Au-PeEL)EBL5577310 035 $a(OCoLC)262680701 035 $a(PPN)123090768 035 $a(EXLCZ)991000000000231894 100 $a20210218d2005 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHypoelliptic estimates and spectral theory for fokker-planck operators and witten laplacians /$fBernard Helffer, Francis Nier 205 $a1st ed. 2005. 210 1$aBerlin, Germany ;$aNew York, United States :$cSpringer,$d[2005] 210 4$d©2005 215 $a1 online resource (X, 209 p.) 225 1 $aLecture notes in mathematics ;$v1862 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-24200-7 320 $aIncludes bibliographical references (pages [195]-203) and index. 327 $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. 330 $aThere has recently been a renewal of interest in Fokker-Planck operators, motivated by problems in statistical physics, in kinetic equations and differential geometry. Compared to more standard problems in the spectral theory of partial differential operators, those operators are not self-adjoint and only hypoelliptic. The aim of the analysis is to give, as generally as possible, an accurate qualitative and quantitative description of the exponential return to the thermodynamical equilibrium. While exploring and improving recent results in this direction this volume proposes a review of known techniques on: the hypoellipticity of polynomial of vector fields and its global counterpart; the global Weyl-Hörmander pseudo-differential calculus, the spectral theory of non-self-adjoint operators, the semi-classical analysis of Schrödinger-type operators, the Witten complexes and the Morse inequalities. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1862. 606 $aSpectral theory (Mathematics) 606 $aHypoelliptic operators 615 0$aSpectral theory (Mathematics) 615 0$aHypoelliptic operators. 676 $a510 700 $aHelffer$b Bernard$052445 702 $aNier$b Francis 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466484303316 996 $aHypoelliptic estimates and spectral theory for fokker-planck operators and witten laplacians$92831099 997 $aUNISA