The book concisely presents the fundamental aspects of the theory
of operators on Hilbert spaces. The topics covered include
functional calculus and spectral theorems, compact operators, trace
class and Hilbert-Schmidt operators, self-adjoint extensions of
symmetric operators, and one-parameter groups of operators. The
exposition of the material on unbounded operators is based on a
novel tool, called the z-transform, which provides a way to encode
full information about unbounded operators in bounded ones, hence
making many technical aspects of the theory less involved.
General
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