Heat kernels and spectral theory
著者
書誌事項
Heat kernels and spectral theory
（Cambridge tracts in mathematics, 92）
Cambridge University Press, 1990, c1989
1st pbk. ed
- : pbk
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注記
Includes bibliographical references (p. [187]-194) and index
内容説明・目次
内容説明
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 Schroedinger 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.
目次
- Preface
- 1. Introductory concepts
- 2. Logarithmic Sobolev inequalities
- 3. Gaussian bounds on heat kernels
- 4. Boundary behaviour
- 5. Riemannian manifolds
- References
- Notation index
- Index.
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