An Introduction to Operators on the Hardy-Hilbert Space [electronic resource] / by Rubén A. Martínez-Avendaño, Peter Rosenthal.
Contributor(s): Rosenthal, Peter [author.] | SpringerLink (Online service)Material type: TextSeries: Graduate Texts in Mathematics: 237Publisher: New York, NY : Springer New York, 2007Description: XII, 220 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780387485782Subject(s): Mathematics | Functional analysis | Functions of complex variables | Operator theory | Mathematics | Operator Theory | Functional Analysis | Functions of a Complex VariableAdditional physical formats: Printed edition:: No titleDDC classification: 515.724 LOC classification: QA329-329.9Online resources: Click here to access online
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The Unilateral Shift and Factorization of Functions -- Toeplitz Operators -- Hankel Operators -- Composition Operators -- Further Reading.
The subject of this book is operator theory on the Hardy space H2, also called the Hardy-Hilbert space. This is a popular area, partially because the Hardy-Hilbert space is the most natural setting for operator theory. A reader who masters the material covered in this book will have acquired a firm foundation for the study of all spaces of analytic functions and of operators on them. The goal is to provide an elementary and engaging introduction to this subject that will be readable by everyone who has understood introductory courses in complex analysis and in functional analysis. The exposition, blending techniques from "soft" and "hard" analysis, is intended to be as clear and instructive as possible. Many of the proofs are very elegant. This book evolved from a graduate course that was taught at the University of Toronto. It should prove suitable as a textbook for beginning graduate students, or even for well-prepared advanced undergraduates, as well as for independent study. There are numerous exercises at the end of each chapter, along with a brief guide for further study which includes references to applications to topics in engineering.