Heat kernels and spectral theory [E-Book] / E.B. Davies.
Davies, E. B., (author)
Cambridge : Cambridge University Press, 1989
1 online resource (ix, 197 pages)
Cambridge tracts in mathematics ; 92
Full Text
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.