Heat Kernels for Elliptic and Sub-elliptic Operators Methods and Techniques /

This monograph is a unified presentation of several theories of finding explicit formulas for heat kernels for both elliptic and sub-elliptic operators. These kernels are important in the theory of parabolic operators because they describe the distribution of heat on a given manifold as well as evol...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριοι συγγραφείς: Calin, Ovidiu (Συγγραφέας), Chang, Der-Chen (Συγγραφέας), Furutani, Kenro (Συγγραφέας), Iwasaki, Chisato (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Boston : Birkhäuser Boston, 2011.
Έκδοση:1.
Σειρά:Applied and Numerical Harmonic Analysis
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
Πίνακας περιεχομένων:
  • Part I. Traditional Methods for Computing Heat Kernels
  • Introduction
  • Stochastic Analysis Method
  • A Brief Introduction to Calculus of Variations
  • The Path Integral Approach
  • The Geometric Method
  • Commuting Operators
  • Fourier Transform Method
  • The Eigenfunctions Expansion Method
  • Part II. Heat Kernel on Nilpotent Lie Groups and Nilmanifolds
  • Laplacians and Sub-Laplacians
  • Heat Kernels for Laplacians and Step 2 Sub-Laplacians
  • Heat Kernel for Sub-Laplacian on the Sphere S^3
  • Part III. Laguerre Calculus and Fourier Method
  • Finding Heat Kernels by Using Laguerre Calculus
  • Constructing Heat Kernel for Degenerate Elliptic Operators
  • Heat Kernel for the Kohn Laplacian on the Heisenberg Group
  • Part IV. Pseudo-Differential Operators
  • The Psuedo-Differential Operators Technique
  • Bibliography
  • Index.