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© 2007

An Introduction to Operators on the Hardy-Hilbert Space

Textbook

Part of the Graduate Texts in Mathematics book series (GTM, volume 237)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Pages 1-35
  3. Pages 95-121
  4. Pages 123-162
  5. Pages 163-195
  6. Pages 197-199
  7. Back Matter
    Pages 201-223

About this book

Introduction

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.

Keywords

Complex analysis Hardy space Hilbert space Operator theory functional analysis

Authors and affiliations

  1. 1.Centro de Investigación en MatemáticasUniversidad Autónoma del Estado de HidalgoPachuca, HidalgoMexico
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada

Bibliographic information

Reviews

From the reviews:

"This text appears as number 237 in the Graduate Texts in Mathematics series published by Springer. … possible textbook for graduate courses, as well as independent study and reference for research. The book is very well written and contains very elegant proofs. … Each chapter in the book has plenty of exercises … . In short: this is a wonderful book, a pleasure to read and use as a text, or add to any mathematician’s ‘collection’ of references to a beautiful and rich subject." (Mihaela Poplicher, MathDL, April, 2007)

"The aim of this book is to provide an introduction to operator theory on the Hardy space H2, also called the Hardy-Hilbert space. … Each chapter ends with a list of exercises and notes and remarks. … The book gives an elementary and brief account of some basic aspects of operators on H2 and can be used as a first introduction to this area." (Takahiko Nakazi, Mathematical Reviews, 2007 k)

"This text is a gentle introduction to the ‘concrete’ operator theory on the Hardy-Hilbert space H2, an important model space for operator theory on function spaces. … Each chapter contains a number of exercises. … Historical notes and remarks are also included. The bibliography is exhaustive and up to date. The book seems completely suitable for a first- or second-year graduate course in function spaces and operator theory … and can probably be adapted to both a basic and a more advanced course." (Dragan Vukotic, Zentralblatt MATH, Vol. 1116 (18), 2007)