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Item Details
| Title:
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OPERATORS, FUNCTIONS, AND SYSTEMS
AN EASY READING |
| Volume: |
Volume 1 |
| By: |
Nikolai K. Nikolski |
| Format: |
Paperback |
| List price:
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£113.00 |
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We believe that this item is permanently unavailable, and so we cannot source
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| ISBN 10: |
0821849336 |
| ISBN 13: |
9780821849330 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
15 January, 2002 |
| Series: |
Mathematical Surveys and Monographs 92 |
| Pages: |
461 |
| Synopsis: |
Together with the companion volume by the same author, Operators, Functions, and Systems: An Easy Reading. Volume 2: Model Operators and Systems, Mathematical Surveys and Monographs, Vol. 93, AMS, 2002, this unique work combines four major topics of modern analysis and its applications: A. Hardy classes of holomorphic functions; B. Spectral theory of Hankel and Toeplitz operators; C. Function models for linear operators and free interpolations; and D. Infinite-dimensional system theory and signal processing. This volume contains Parts A and B. Hardy classes of holomorphic functions is known to be the most powerful tool in complex analysis for a variety of applications, starting with Fourier series, through the Riemann $\zeta$-function, all the way to Wiener's theory of signal processing. Spectral theory of Hankel and Toeplitz operators becomes the supporting pillar for a large part of harmonic and complex analysis and for many of their applications. In this book, moment problems, Nevanlinna-Pick and Caratheodory interpolation, and the best rational approximations are considered to illustrate the power of Hankel and Toeplitz operators.The book is geared toward a wide audience of readers, from graduate students to professional mathematicians, interested in operator theory and functions of a complex variable. The two volumes develop an elementary approach while retaining an expert level that can be applied in advanced analysis and selected applications. Table of Contents: An invitation to Hardy classes/Contents: Foreword to Part A; Invariant subspaces of $L^2(\mu)$; First applications; $H^p$ classes. Canonical factorization; Szego infimum, and generalized Phragmen-Lindelof principle; Harmonic analysis in $L^2(\mathbb{T},\mu)$; Transfer to the half-plane; Time-invariant filtering; Distance formulae and zeros of the Riemann $\zeta$-function. Hankel and Toeplitz operators/Contents: Foreword to Part B; Hankel operators and their symbols; Compact Hankel operators; Applications to Nevanlinna-Pick interpolation; Essential spectrum. The first step: Elements of Toeplitz operators; Essential spectrum.The second step: The Hilbert matrix and other Hankel operators; Hankel and Toeplitz operators associated with moment problems; Singular numbers of Hankel operators; Trace class Hankel operators; Inverse spectral problems, stochastic processes and one-sided invertibility; Bibliography; Author index; Subject index; Symbol index. This is a reprint of the 2002 original. (SURV/92.S) |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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