Partial Differential Equations VII: Spectral Theory of Differential Operators (Encyclopedia of Mathematical Sciences Series), Vol. 64

This "EMS" volume contains a survey of the principles and advanced techniques of the spectral theory of linear differential and pseudodifferential operators in finite-dimensional spaces. The basic notions and theorems are first reviewed and followed by a comprehensive presentation of a variety of advanced approaches such as the factorization method, the variational techniques, the approximate spectral projection method, and the probabilistic method, to name a few. Special attention is devoted to the spectral properties of Schrodinger and Dirac operators and of other operators as well. In addition, a special section of Sunada's recent solution of Kac's celebrated problem of whether or not "one can hear the shape of a drum" is included.Shubin, M. A. is the author of 'Partial Differential Equations VII: Spectral Theory of Differential Operators (Encyclopedia of Mathematical Sciences Series), Vol. 64' with ISBN 9780387546773 and ISBN 0387546774.