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Hypoelliptic estimates and spectral theory for Fokker-Planck operators and Witten Laplacians

Author: Bernard Helffer; Francis Nier
Publisher: Berlin : Springer, ©2005.
Series: Lecture notes in mathematics (Springer-Verlag), 1862.
Edition/Format:   Print book : EnglishView all editions and formats
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Bernard Helffer; Francis Nier
ISBN: 3540242007 9783540242000 9783540315537 3540315535
OCLC Number: 58527852
Description: x, 209 pages : illustrations ; 24 cm.
Contents: 1. Introduction.- 2. Kohn's Proof of the Hypoellipticity of the Hoermander Operators.- 3. Compactness Criteria for the Resolvent of Schroedinger Operators.- 4. Global Pseudo-differential Calculus.- 5. Analysis of some Fokker-Planck Operator.- 6. Return to Equillibrium for the Fokker-Planck Operator.- 7. Hypoellipticity and nilpotent groups.- 8. Maximal Hypoellipticity for Polynomial of Vector Fields and Spectral Byproducts.- 9. On Fokker-Planck Operators and Nilpotent Techniques.- 10. Maximal Microhypoellipticity for Systems and Applications to Witten Laplacians.- 11. Spectral Properties of the Witten-Laplacians in Connection with Poincare inequalities for Laplace Integrals.- 12. Semi-classical Analysis for the Schroedinger Operator: Harmonic Approximation.- 13. Decay of Eigenfunctions and Application to the Splitting.- 14. Semi-classical Analysis and Witten Laplacians: Morse Inequalities.- 15. Semi-classical Analysis and Witten Laplacians: Tunneling Effects.- 16. Accurate Asymptotics for the Exponentially Small Eigenvalues of the Witten Laplacian.- 17. Application to the Fokker-Planck Equation.- 18. Epilogue.- References.- Index.
Series Title: Lecture notes in mathematics (Springer-Verlag), 1862.
Responsibility: Bernard Helffer, Francis Nier.
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From the reviews of the first edition:"The aim of this text is to give an account of how the known techniques from partial differential equations and spectral theory can be applied for the analysis Read more...

 
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