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

• Main Authors: Calin, Ovidiu (Author), Chang, Der-Chen (Author), Furutani, Kenro (Author), Iwasaki, Chisato (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston : Birkhäuser Boston, 2011.
• Edition: 1.
• Series: Applied and Numerical Harmonic Analysis
• Subjects: Mathematics.; Harmonic analysis.; Operator theory.; Partial differential equations.; Differential geometry.; Probabilities.; Physics.; Partial Differential Equations.; Mathematical Methods in Physics.; Operator Theory.; Differential Geometry.; Probability Theory and Stochastic Processes.; Abstract Harmonic Analysis.

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...

Table of Contents:

• 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.