Harmonic Analysis of Operators on Hilbert Space
(Sprache: Englisch)
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...
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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, including 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.
Klappentext zu „Harmonic Analysis of Operators on Hilbert Space “
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.
Inhaltsverzeichnis zu „Harmonic Analysis of Operators on Hilbert Space “
Contractions and Their Dilations.- Geometrical and Spectral Properties of Dilations.- Functional Calculus.- Extended Functional Calculus.- Operator-Valued Analytic Functions.- Functional Models.- Regular Factorizations and Invariant Subspaces.- Weak Contractions.- The Structure of C1.-Contractions.- The Structure of Operators of Class C0.
Autoren-Porträt von Béla Sz Nagy, Ciprian Foias, Hari Bercovici, László Kérchy
Béla Szkefalvi-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 the Szeged University. He made important contributions to operator theory, many of them represented in this monograph.
Bibliographische Angaben
- Autoren: Béla Sz Nagy , Ciprian Foias , Hari Bercovici , László Kérchy
- 2010, 2nd ed., XIV, 478 Seiten, Masse: 23,4 x 15,9 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 1441960937
- ISBN-13: 9781441960931
- Erscheinungsdatum: 01.09.2010
Sprache:
Englisch
Rezension zu „Harmonic Analysis of Operators on Hilbert Space “
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)
Pressezitat
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)
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