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Harmonic Analysis of Operators on Hilbert Space

  • Béla Sz.-Nagy
  • Ciprian Foias
  • Hari Bercovici
  • László Kérchy

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Béla Sz.-Nagy, Hari Bercovici, Ciprian Foias, László Kérchy
    Pages 1-58
  3. Béla Sz.-Nagy, Hari Bercovici, Ciprian Foias, László Kérchy
    Pages 59-102
  4. Béla Sz.-Nagy, Hari Bercovici, Ciprian Foias, László Kérchy
    Pages 103-157
  5. Béla Sz.-Nagy, Hari Bercovici, Ciprian Foias, László Kérchy
    Pages 159-187
  6. Béla Sz.-Nagy, Hari Bercovici, Ciprian Foias, László Kérchy
    Pages 189-241
  7. Béla Sz.-Nagy, Hari Bercovici, Ciprian Foias, László Kérchy
    Pages 243-287
  8. Béla Sz.-Nagy, Hari Bercovici, Ciprian Foias, László Kérchy
    Pages 289-330
  9. Béla Sz.-Nagy, Hari Bercovici, Ciprian Foias, László Kérchy
    Pages 331-359
  10. Béla Sz.-Nagy, Hari Bercovici, Ciprian Foias, László Kérchy
    Pages 361-396
  11. Béla Sz.-Nagy, Hari Bercovici, Ciprian Foias, László Kérchy
    Pages 397-440
  12. Back Matter
    Pages 441-474

About this book

Introduction

The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis.  The first edition of this book was an account of the progress done in this direction in 1950-70.  Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory.

This second edition, in addition to revising and amending the original text, focuses on further developments of the theory.  Specifically, the last two chapters of the book continue and complete the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective.  For both of these classes, a wealth of material on structure, classification and invariant subspaces is included in Chapters IX and X.  Several chapters conclude with a sketch of other developments related with (and developing) the material of the first edition.

Keywords

Functional Calculus Hilbert Space Invariant Subspaces Operator Valued Analytic Functions Unitary Dilations analysis harmonic analysis

Authors and affiliations

  • Béla Sz.-Nagy
    • 1
  • Ciprian Foias
    • 2
  • Hari Bercovici
    • 3
  • László Kérchy
    • 4
  1. 1.SzegedHungary
  2. 2.Dept. MathematicsTexas A & M UniversityCollege StationUSA
  3. 3.Dept. MathematicsIndiana UniversityBloomingtonUSA
  4. 4.Bolyai InstituteUniversity of SzegedSzegedHungary

Bibliographic information