This book is an introduction to the theory of partial differential
operators. It assumes that the reader has a knowledge of
introductory functional analysis, up to the spectral theorem for
bounded linear operators on Banach spaces. However, it describes
the theory of Fourier transforms and distributions as far as is
needed to analyse the spectrum of any constant coefficient partial
differential operator. A completely new proof of the spectral
theorem for unbounded self-adjoint operators is followed by its
application to a variety of second-order elliptic differential
operators, from those with discrete spectrum to Schroedinger
operators acting on L2(RN). The book contains a detailed account of
the application of variational methods to estimate the eigenvalues
of operators with measurable coefficients defined by the use of
quadratic form techniques. This book could be used either for
self-study or as a course text, and aims to lead the reader to the
more advanced literature on the subject.
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