The Resource Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians, by Bernard Helffer, Francis Nier, (electronic resource)

Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians, by Bernard Helffer, Francis Nier, (electronic resource)

Label
Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians
Title
Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians
Statement of responsibility
by Bernard Helffer, Francis Nier
Creator
Contributor
Author
Provider
Subject
Language
eng
Summary
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
Member of
http://library.link/vocab/creatorName
Helffer, Bernard
Image bit depth
0
LC call number
QA370-380
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
  • Nier, Francis
  • SpringerLink
Series statement
Lecture Notes in Mathematics,
Series volume
1862
http://library.link/vocab/subjectName
  • Mathematics
  • Global analysis
  • Differential equations, partial
  • Quantum theory
  • Statistics
  • Mathematics
  • Partial Differential Equations
  • Global Analysis and Analysis on Manifolds
  • Quantum Physics
  • Statistics for Engineering, Physics, Computer Science, Chemistry & Geosciences
Label
Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians, by Bernard Helffer, Francis Nier, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Dimensions
unknown
Extent
X, 209 p.
File format
multiple file formats
Form of item
electronic
Isbn
9783540315537
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/b104762
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-540-31553-7
Label
Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians, by Bernard Helffer, Francis Nier, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Dimensions
unknown
Extent
X, 209 p.
File format
multiple file formats
Form of item
electronic
Isbn
9783540315537
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/b104762
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-540-31553-7

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