Operators, Functions, and Systems, Volume 1; Hardy, Hankel, and Toeplitz : An Easy Reading Paperback / softback
by Nikolai K. Nikolski
Part of the Mathematical Surveys and Monographs series
Paperback / softback
Description
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)
Information
-
Out of Stock - We are unable to provide an estimated availability date for this product
- Format:Paperback / softback
- Pages:461 pages
- Publisher:American Mathematical Society
- Publication Date:30/01/2002
- Category:
- ISBN:9780821849330
Information
-
Out of Stock - We are unable to provide an estimated availability date for this product
- Format:Paperback / softback
- Pages:461 pages
- Publisher:American Mathematical Society
- Publication Date:30/01/2002
- Category:
- ISBN:9780821849330
