LEADER 04134nam 2200661 450 001 9910483993903321 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 $a9910483993903321 996 $aHypoelliptic estimates and spectral theory for fokker-planck operators and witten laplacians$92831099 997 $aUNINA LEADER 03093nam 2200673Ia 450 001 9910964711603321 005 20250609110831.0 010 $a1-281-49351-1 010 $a9786611493516 010 $a0-387-73988-2 024 7 $a10.1007/978-0-387-73988-5 035 $a(CKB)1000000000440683 035 $a(EBL)372703 035 $a(OCoLC)272298664 035 $a(SSID)ssj0000241515 035 $a(PQKBManifestationID)11199801 035 $a(PQKBTitleCode)TC0000241515 035 $a(PQKBWorkID)10316525 035 $a(PQKB)11121003 035 $a(DE-He213)978-0-387-73988-5 035 $a(Au-PeEL)EBL372703 035 $a(CaPaEBR)ebr10501599 035 $a(CaONFJC)MIL149351 035 $a(PPN)127046445 035 $a(MiAaPQ)EBC372703 035 $a(MiAaPQ)EBC4418275 035 $a(EXLCZ)991000000000440683 100 $a20071121d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aScalar and asymptotic scalar derivatives $etheory and applications /$fby George Isac, Sandor Zoltan Nemeth 205 $a1st ed. 2008. 210 $aNew York $cSpringer$dc2008 215 $a1 online resource (252 p.) 225 1 $aSpringer optimization and its applications ;$vv. 13 300 $aDescription based upon print version of record. 311 08$a1-4419-4484-2 311 08$a0-387-73987-4 320 $aIncludes bibliographical references and index. 327 $aScalar Derivatives in Euclidean Spaces -- Asymptotic Derivatives and Asymptotic Scalar Derivatives -- Scalar Derivatives in Hilbert Spaces -- Scalar Derivatives in Banach Spaces -- Monotone Vector Fields on Riemannian Manifolds and Scalar Derivatives. 330 $aThis book is devoted to the study of scalar and asymptotic scalar derivatives and their applications to some problems in nonlinear analysis, Riemannian geometry, and applied mathematics. The theoretical results are developed in particular with respect to the study of complementarity problems, monotonicity of nonlinear mappings ,and non-gradient type monotonicity on Riemannian manifolds. Scalar and Asymptotic Derivatives: Theory and Applications also presents the material in relation to Euclidean spaces, Hilbert spaces, Banach spaces, Riemannian manifolds, and Hadamard manifolds. This book is intended for researchers and graduate students working in the fields of nonlinear analysis, Riemannian geometry, and applied mathematics. In addition, it fills a gap in the literature as the first book to appear on the subject. 410 0$aSpringer optimization and its applications ;$vv. 13. 606 $aNumerical analysis 606 $aScalar field theory 615 0$aNumerical analysis. 615 0$aScalar field theory. 676 $a518 700 $aIsac$b George$060359 701 $aNemeth$b Sandor Zoltan$01823686 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910964711603321 996 $aScalar and asymptotic scalar derivatives$94390520 997 $aUNINA