Composition Operators: and Classical Function Theory (Universitext: Tracts in Mathematics) - Tapa blanda

Shapiro, Joel H. H.

 
9780387940670: Composition Operators: and Classical Function Theory (Universitext: Tracts in Mathematics)
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ISBN 10: 0387940677 ISBN 13: 9780387940670
Editorial: Springer, 1993

Sinopsis

The study of composition operators forges links between fundamental properties of linear operators and beautiful results from the classical theory of analytic functions. This book provides a self-contained introduction to both the subject and its function-theoretic underpinnings, and features a development accessible to anyone who has studied basic graduate level real and complex analysis. The work traces how such operator-theoretic issues as boundedness, compactness, and cyclicity, when studied in the context of composition operators, evolve into questions about subordination, value-distribution, angular derivatives, iteration, and functional equations; and it carefully develops each of these classical topics.

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Reseña del editor

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.

Reseña del editor

The study of composition operators forges links between fundamental properties of linear operators and beautiful results from the classical theory of analytic functions. This book provides a self-contained introduction to both the subject and its function-theoretic underpinnings. The development is geometrically motivated, and accessible to anyone who has studied basic graduate-level real and complex analysis. The work explores how operator-theoretic issues such as boundedness, compactness, and cyclicity evolve - in the setting of composition operators on the Hilbert space H2 into questions about subordination, value distribution, angular derivatives, iteration, and functional equations. Each of these classical topics is developed fully, and particular attention is paid to their common geometric heritage as descendants of the Schwarz Lemma.

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Editorial
Springer
Año de publicación
1993
Idioma
Inglés
ISBN 10 
0387940677
ISBN 13 
9780387940670
Encuadernación
Tapa blanda
Número de páginas
244
Contacto del fabricante
no disponible
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9783540940678: Composition Operators and Classical Function Theory (Universitext)

Edición Destacada

ISBN 10:  3540940677 ISBN 13:  9783540940678
Editorial: Springer-Verlag Berlin and Heide..., 1993
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