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Item Details
| Title:
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ORTHOGONAL POLYNOMIALS ON THE UNIT CIRCLE
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| Volume: |
Classical Theory |
| By: |
Barry Simon |
| Format: |
Hardback |
| List price:
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£69.95 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
0821834460 |
| ISBN 13: |
9780821834466 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
26 November, 2004 |
| Series: |
Colloquium Publications No. 54.1 |
| Pages: |
466 |
| Description: |
Presents an overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. This book discusses topics such as asymptotics of Toeplitz determinants (Szego's theorems), and limit theorems for the density of the zeros of orthogonal polynomials. |
| Synopsis: |
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. |
| Illustrations: |
Illustrations |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Non-returnable |
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