Operator Theory by Example (Oxford Graduate Texts in Mathematics)

Aimed at graduate students, this textbook provides an accessible and comprehensive introduction to operator theory. Rather than discuss the subject in the abstract, this textbook covers the subject through twenty examples of a wide variety of operators, discussing the norm, spectrum, commutant, invariant subspaces, and interesting properties of each operator.\nThe text is supplemented by over 600 end-of-chapter exercises, designed to help the reader master the topics covered in the chapter, as well as providing an opportunity to further explore the vast operator theory literature. Each chapter also contains well-researched historical facts which place each chapter within the broader context of the development of the field as a whole.

Science & Math

Garcia, Stephan Ramon

Ross, William T.

Mashreghi, Javad

Mathematics

Oxford University Press

Voice Culture and Elocution.

This is a pre-1923 historical reproduction that was curated for quality. Quality assurance was conducted on each of these books in an attempt to remove books with imperfections introduced by the digitization process. Though we have made best efforts - the books may have occasional errors that do not impede the reading experience. We believe this work is culturally important and have elected to bring the book back into print as part of our continuing commitment to the preservation of printed works worldwide.

History

World

BiblioLife

The theory of generalized analytic continuation studies continuations of meromorphic functions in situations where traditional theory says there is a natural boundary. This broader theory touches on a remarkable array of topics in classical analysis, as described in the book. This book addresses the following questions: (1) When can we say, in some reasonable way, that component functions of a meromorphic function on a disconnected domain, are ``continuations'' of each other? (2) What role do such ``continuations'' play in certain aspects of approximation theory and operator theory? The authors use the strong analogy with the summability of divergent series to motivate the subject. In this vein, for instance, theorems can be described as being ``Abelian'' or ``Tauberian''. The introductory overview carefully explains the history and context of the theory. The authors begin with a review of the works of Poincare, Borel, Wolff, Walsh, and Goncar, on continuation properties of ``Borel series'' and other meromorphic functions that are limits of rapidly convergent sequences of rational functions. They then move on to the work of Tumarkin, who looked at the continuation properties of functions in the classical Hardy space of the disk in terms of the concept of ``pseudocontinuation''. Tumarkin's work was seen in a different light by Douglas, Shapiro, and Shields in their discovery of a characterization of the cyclic vectors for the backward shift operator on the Hardy space. The authors cover this important concept of ``pseudocontinuation'' quite thoroughly since it appears in many areas of analysis. They also add a new and previously unpublished method of ``continuation'' to the list, based on formal multiplication of trigonometric series, which can be used to examine the backward shift operator on many spaces of analytic functions. The book attempts to unify the various types of ``continuations'' and suggests some interesting open questions.

Generalized Analytic Continuation

Shapiro, Harold S.

Amer Mathematical Society

The study of model spaces, the closed invariant subspaces of the backward shift operator, is a vast area of research with connections to complex analysis, operator theory and functional analysis. This self-contained text is the ideal introduction for newcomers to the field. It sets out the basic ideas and quickly takes the reader through the history of the subject before ending up at the frontier of mathematical analysis. Open questions point to potential areas of future research, offering plenty of inspiration to graduate students wishing to advance further.

Introduction to Model Spaces and their Operators (Cambridge Studies in Advanced Mathematics, Series Number 148)

Cambridge University Press

Voice Culture and Elocution

Nabu Press

Voice Culture And Elocution.

Reference

Leiserson Press

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