Overview
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.
Full Product Details
Author: Francis Nier ,
Bernard Helffer
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition: 2005 ed.
Volume: 1862
Dimensions:
Width: 15.50cm
, Height: 1.20cm
, Length: 23.50cm
Weight: 0.720kg
ISBN: 9783540242000
ISBN 10: 3540242007
Pages: 209
Publication Date: 11 February 2005
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: In Print
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.
Reviews
From the reviews of the first edition: <p> 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 of Fokker-Plank operators or Witten Laplacians a ] . This synthetic text is very challenging and useful for researchers in partial differential equations, probability theory and mathematical physics. (Viorel Iftimie, Zentralblatt MATH, Vol. 1072, 2005)
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 of Fokker-Plank operators or Witten Laplacians … . This synthetic text is very challenging and useful for researchers in partial differential equations, probability theory and mathematical physics."" (Viorel Iftimie, Zentralblatt MATH, Vol. 1072, 2005)
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 of Fokker-Plank operators or Witten Laplacians ... . This synthetic text is very challenging and useful for researchers in partial differential equations, probability theory and mathematical physics. (Viorel Iftimie, Zentralblatt MATH, Vol. 1072, 2005)
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 of Fokker-Plank operators or Witten Laplacians ! . This synthetic text is very challenging and useful for researchers in partial differential equations, probability theory and mathematical physics. (Viorel Iftimie, Zentralblatt MATH, Vol. 1072, 2005)
"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 of Fokker-Plank operators or Witten Laplacians … . This synthetic text is very challenging and useful for researchers in partial differential equations, probability theory and mathematical physics."" (Viorel Iftimie, Zentralblatt MATH, Vol. 1072, 2005)"
