Heat Kernels and Spectral Theory [Paperback]

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