Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians

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 an...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Nier, Francis (Autor), Helffer, Bernard (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2005.
Edición:1st ed. 2005.
Colección:Lecture Notes in Mathematics, 1862
Temas:
Differential equations.
Thermodynamics.
Heat engineering.
Heat transfer.
Mass transfer.
Geometry.
Global analysis (Mathematics).
Manifolds (Mathematics).
Quantum physics.
Statistics .
Differential Equations.
Engineering Thermodynamics, Heat and Mass Transfer.
Global Analysis and Analysis on Manifolds.
Quantum Physics.
Statistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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