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

Ovidiu Calin, Der-Chen Chang, Kenro Furutani, and Chisato Iwasaki
Publisher: 
Birkhäuser
Publication Date: 
2011
Number of Pages: 
433
Format: 
Hardcover
Series: 
Applied and Numerical Harmonic Analysis
Price: 
124.00
ISBN: 
9780817649944
Category: 
Monograph
We do not plan to review this book.

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.

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