Joel H. Shapiro's Books

Cyclic Phenomena for Composition Operators

By: Paul Bourdon,Joel H. Shapiro

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Cyclic Phenomena for Composition Operators

By: Paul Bourdon,Joel H. Shapiro

We undertake a systematic study of cyclic phenomena for composition operators. Our work shows that composition operators exhibit strikingly diverse types of cyclic behavior, and it connects this behavior with classical problems involving complex polynomial approximation and analytic functional equations.

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Page Count

122

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821806300

ISBN 13

9780821806302

Composition Operators

and Classical Function Theory

By: Joel H. Shapiro

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Composition Operators

and Classical Function Theory

By: Joel H. Shapiro

The study of composition operators links some of the most basic questions you can ask about linear operators with beautiful classical results from analytic-function theory. The process invests old theorems with new mean ings, and bestows upon functional analysis an intriguing class of concrete linear operators. Best of all, the subject can be appreciated by anyone with an interest in function theory or functional analysis, and a background roughly equivalent to the following twelve chapters of Rudin's textbook Real and Complex Analysis [Rdn '87]: Chapters 1-7 (measure and integra tion, LP spaces, basic Hilbert and Banach space theory), and 10-14 (basic function theory through the Riemann Mapping Theorem). In this book I introduce the reader to both the theory of composition operators, and the classical results that form its infrastructure. I develop the subject in a way that emphasizes its geometric content, staying as much as possible within the prerequisites set out in the twelve fundamental chapters of Rudin's book. Although much of the material on operators is quite recent, this book is not intended to be an exhaustive survey. It is, quite simply, an invitation to join in the fun. The story goes something like this.

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Page Count

229

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461208874

ISBN 13

9781461208877

Volterra Adventures

By: Joel H. Shapiro

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Volterra Adventures

By: Joel H. Shapiro

This book introduces functional analysis to undergraduate mathematics students who possess a basic background in analysis and linear algebra. By studying how the Volterra operator acts on vector spaces of continuous functions, its readers will sharpen their skills, reinterpret what they already know, and learn fundamental Banach-space techniques—all in the pursuit of two celebrated results: the Titchmarsh Convolution Theorem and the Volterra Invariant Subspace Theorem. Exercises throughout the text enhance the material and facilitate interactive study.

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Page Count

240

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470441160

ISBN 13

9781470441166

A Fixed-Point Farrago

By: Joel H. Shapiro

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A Fixed-Point Farrago

By: Joel H. Shapiro

This text provides an introduction to some of the best-known fixed-point theorems, with an emphasis on their interactions with topics in analysis. The level of exposition increases gradually throughout the book, building from a basic requirement of undergraduate proficiency to graduate-level sophistication. Appendices provide an introduction to (or refresher on) some of the prerequisite material and exercises are integrated into the text, contributing to the volume’s ability to be used as a self-contained text. Readers will find the presentation especially useful for independent study or as a supplement to a graduate course in fixed-point theory. The material is split into four parts: the first introduces the Banach Contraction-Mapping Principle and the Brouwer Fixed-Point Theorem, along with a selection of interesting applications; the second focuses on Brouwer’s theorem and its application to John Nash’s work; the third applies Brouwer’s theorem to spaces of infinite dimension; and the fourth rests on the work of Markov, Kakutani, and Ryll–Nardzewski surrounding fixed points for families of affine maps.

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Page Count

225

Publisher

Springer

Published Date

ISBN 10

3319279785

ISBN 13

9783319279787

Volterra Adventures

By: Joel H. Shapiro

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Volterra Adventures

By: Joel H. Shapiro

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Solve jigsaw puzzle

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Page Count

240

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470441160

ISBN 13

9781470441166

Book's by Joel H. Shapiro

Cyclic Phenomena for Composition Operators

Cyclic Phenomena for Composition Operators

Composition Operators

Composition Operators

Volterra Adventures

Volterra Adventures

A Fixed-Point Farrago

A Fixed-Point Farrago

Volterra Adventures

Volterra Adventures

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