Partial Differential Equations VII: Spectral Theory of Differential Operators

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 Schrödinger 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', published 1994 under ISBN 9783540546771 and ISBN 3540546774.