An advanced monograph on a central topic in the theory of differential equations, Heat Kernels and Spectral Theory investigates the theory of second-order elliptic operators. While the study of the heat equation is a classical subject, this book analyses the improvements in our quantitative understanding of heat kernels. The author considers variable coefficient operators on regions in Euclidean space and Laplace-Beltrami operators on complete Riemannian manifolds. He also includes results pertaining to the heat kernels of Schrödinger operators; such results will be of particular interest to mathematical physicists, and relevant too to those concerned with properties of Brownian motion and other diffusion processes.
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- Date Published: February 1991
- format: Paperback
- isbn: 9780521409971
- length: 208 pages
- dimensions: 227 x 150 x 13 mm
- weight: 0.323kg
- availability: Available
Table of Contents
1. Introductory concepts
2. Logarithmic Sobolev inequalities
3. Gaussian bounds on heat kernels
4. Boundary behaviour
5. Riemannian manifolds
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