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...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Calin, Ovidiu (Autor), Chang, Der-Chen (Autor), Furutani, Kenro (Autor), Iwasaki, Chisato (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2011.
Edición:1st ed. 2011.
Colección:Applied and Numerical Harmonic Analysis,
Temas:
Differential equations.
Mathematical physics.
Operator theory.
Geometry, Differential.
Probabilities.
Harmonic analysis.
Differential Equations.
Mathematical Methods in Physics.
Operator Theory.
Differential Geometry.
Probability Theory.
Abstract Harmonic Analysis.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

Ejemplares similares