Universitext

Harmonic Analysis of Operators on Hilbert Space

Authors: Sz Nagy, B., Foias, C., Bercovici, H., Kérchy, L.

  • 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
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eBook $54.99
price for USA (gross)
  • ISBN 978-1-4419-6094-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $74.95
price for USA
  • ISBN 978-1-4419-6093-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

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.

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)

Table of contents (10 chapters)

  • Contractions and Their Dilations

    Sz.-Nagy, Béla (et al.)

    Pages 1-58

  • Geometrical and Spectral Properties of Dilations

    Sz.-Nagy, Béla (et al.)

    Pages 59-102

  • Functional Calculus

    Sz.-Nagy, Béla (et al.)

    Pages 103-157

  • Extended Functional Calculus

    Sz.-Nagy, Béla (et al.)

    Pages 159-187

  • Operator-Valued Analytic Functions

    Sz.-Nagy, Béla (et al.)

    Pages 189-241

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-1-4419-6094-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $74.95
price for USA
  • ISBN 978-1-4419-6093-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Harmonic Analysis of Operators on Hilbert Space
Authors
Series Title
Universitext
Copyright
2010
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+BusinessMedia, LLC
eBook ISBN
978-1-4419-6094-8
DOI
10.1007/978-1-4419-6094-8
Softcover ISBN
978-1-4419-6093-1
Series ISSN
0172-5939
Edition Number
2
Number of Pages
XIV, 478
Number of Illustrations and Tables
1 b/w illustrations
Topics