Harmonic Analysis of Operators on Hilbert ...

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Beschreibung

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.
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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.

Über den Autor

Béla Sz¿kefalvi-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.

Zusammenfassung

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, 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.

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2010
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xiv 478 S. 1 s/w Illustr. 478 p. 1 illus.
ISBN-13:	9781441960931
ISBN-10:	1441960937
Sprache:	Englisch
Herstellernummer:	12650378
Einband:	Kartoniert / Broschiert
Autor:	Sz Nagy, Béla Foias, Ciprian Bercovici, Hari Kérchy, László
Auflage:	2nd 2010 edition
Hersteller:	Springer New York Springer US, New York, N.Y.
Maße:	236 x 158 x 33 mm
Von/Mit:	Béla Sz Nagy (u. a.)
Erscheinungsdatum:	01.09.2010
Gewicht:	0,711 kg

Artikel-ID: 107448647

Über den Autor

Zusammenfassung

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, 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.

Inhaltsverzeichnis

Details

Erscheinungsjahr:	2010
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xiv 478 S. 1 s/w Illustr. 478 p. 1 illus.
ISBN-13:	9781441960931
ISBN-10:	1441960937
Sprache:	Englisch
Herstellernummer:	12650378
Einband:	Kartoniert / Broschiert
Autor:	Sz Nagy, Béla Foias, Ciprian Bercovici, Hari Kérchy, László
Auflage:	2nd 2010 edition
Hersteller:	Springer New York Springer US, New York, N.Y.
Maße:	236 x 158 x 33 mm
Von/Mit:	Béla Sz Nagy (u. a.)
Erscheinungsdatum:	01.09.2010
Gewicht:	0,711 kg