Heat Kernels and Spectral Theory investigates the theory of second-order elliptic operators.
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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.
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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