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Harmonic Analysis of Operators on Hilbert Space

  • Textbook
  • © 2010

Overview

Authors:
  1. Béla Sz.-Nagy

    1. Szeged, Hungary

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  2. Ciprian Foias

    1. Dept. Mathematics, Texas A & M University, College Station, USA

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  3. Hari Bercovici

    1. Dept. Mathematics, Indiana University, Bloomington, USA

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  4. László Kérchy

    1. Bolyai Institute, University of Szeged, Szeged, Hungary

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  • Fully updated and revised second edition
  • Explores harmonic analysis techniques for the study of the mathematical concept of Hilbert space
  • Focusing mainly on operator theories and developments, the text discusses two specific operator classes
  • Includes supplementary material: sn.pub/extras

Part of the book series: Universitext (UTX)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Contractions and Their Dilations

    • Béla Sz.-Nagy, Hari Bercovici, Ciprian Foias, László Kérchy
    Pages 1-58

  3. Geometrical and Spectral Properties of Dilations

    • Béla Sz.-Nagy, Hari Bercovici, Ciprian Foias, László Kérchy
    Pages 59-102

  4. Functional Calculus

    • Béla Sz.-Nagy, Hari Bercovici, Ciprian Foias, László Kérchy
    Pages 103-157

  5. Extended Functional Calculus

    • Béla Sz.-Nagy, Hari Bercovici, Ciprian Foias, László Kérchy
    Pages 159-187

  6. Operator-Valued Analytic Functions

    • Béla Sz.-Nagy, Hari Bercovici, Ciprian Foias, László Kérchy
    Pages 189-241

  7. Functional Models

    • Béla Sz.-Nagy, Hari Bercovici, Ciprian Foias, László Kérchy
    Pages 243-287

  8. Regular Factorizations and Invariant Subspaces

    • Béla Sz.-Nagy, Hari Bercovici, Ciprian Foias, László Kérchy
    Pages 289-330

  9. Weak Contractions

    • Béla Sz.-Nagy, Hari Bercovici, Ciprian Foias, László Kérchy
    Pages 331-359

  10. The Structure of C 1.-Contractions

    • Béla Sz.-Nagy, Hari Bercovici, Ciprian Foias, László Kérchy
    Pages 361-396

  11. The Structure of Operators of Class C 0

    • Béla Sz.-Nagy, Hari Bercovici, Ciprian Foias, László Kérchy
    Pages 397-440

  12. Back Matter

    Pages 441-474
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Keywords

About this book

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.

Reviews

From the reviews of the second edition:

“The second edition, with coauthors H. Bercovici and L. Kérchy, is a revised and expanded version of the original work. The book presents a theory of contraction operators based on the notion of a minimal unitary dilation. … The second edition of Harmonic analysis of operators on Hilbert space is a timely update and enlargement of the original work. It should remain a valuable source for the theory of contraction operators for many years to come.” (J. Rovnyak, Mathematical Reviews, Issue 2012 b)

Authors and Affiliations

  • Szeged, Hungary

    Béla Sz.-Nagy

  • Dept. Mathematics, Texas A & M University, College Station, USA

    Ciprian Foias

  • Dept. Mathematics, Indiana University, Bloomington, USA

    Hari Bercovici

  • Bolyai Institute, University of Szeged, Szeged, Hungary

    László Kérchy

About the authors

Béla Szőkefalvi-Nagy (1913-1998) was a famed mathematician for his work in functional analysis and operator theory. He was the recipient of the Lomonosov Medal in 1979. Ciprian Ilie Foias is currently a distinguished professor in the department of mathematics at Texas A&M University in College Station. He is well known for his work in operator theory, infinite dimensional dynamical systems, ergodic theory, as well as applications in such diverse fields as control theory, mathematical biology and mathematical economics. Among many other honors, Foias was awarded the Norbert Wiener Prize in applied Mathematics in 1995. Hari Bercovici is currently a professor of mathematics at Indiana University. He works in operator theory and function theory. László Kérchy is the director of the Bolyai Institute at Szeged University. He made important contributions to operator theory, many of them represented in this monograph.

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