This book is an elementary introduction to non-classical spectral theory. After the basic definitions and a reduction to the study of the functional model the discussion will be centered around the simplest variant of such a model which, formally speaking, comprises only the class of contraction operators with a one- dimensional rank of non-unitarity (rank(/ - T*T) = rank(/ - TT*)= 1). The main emphasis is on the technical side of the subject, the book being mostly devoted to a development of the analytical machinery of spectral theory rather than to this discipline itself.
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