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Inhaltsangabe
This two-part volume gives a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of one-dimensional Schrodinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szego's theorems), limit theorems for the density of the zeros of orthogonal polynomials, matrix representations for multiplication by $z$ (CMV matrices), periodic Verblunsky coefficients from the point of view of meromorphic functions on hyperelliptic surfaces, and connections between the theories of orthogonal polynomials on the unit circle and on the real line. The book is suitable for graduate students and researchers interested in analysis.
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This two-part volume gives a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of one-dimensional Schrodinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szego's theorems), limit theorems for the density of the zeros of orthogonal polynomials, matrix representations for multiplication by $z$ (CMV matrices), periodic Verblunsky coefficients from the point of view of meromorphic functions on hyperelliptic surfaces, and connections between the theories of orthogonal polynomials on the unit circle and on the real line. The book is suitable for graduate students and researchers interested in analysis.
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Orthogonal Polynomials On The Unit Circle, Part 2: Spectoral Theory.
Verlag:
American Mathematical Society, 2004
ISBN 10: 0821836757
ISBN 13: 9780821836750
Gebraucht
Hardcover
Anbieter: Antiquariat Bernhardt, Kassel, Deutschland
Verkäuferbewertung 5 von 5 Sternen
gebundene Ausgabe. Zustand: Gut. American Mathematical Society, Colloquium Publications, Volume 54, Part 2. Zust: Gutes Exemplar. Einband berieben. Mit Vorbesitzereintrag. XXI, 577 Seiten, Englisch 1250g. Bestandsnummer des Verkäufers 492272
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