Are you between 5 and 25? If so, enter the Wicked Young Writer Awards NOW - click here for details...

likeyoulove debuts of the month
Search our site
Last Letter from Istanbul by Lucy Foley Read the opening extract of the brand new Lucy Foley book before its publication on 19/03/2018

Operators, Functions, and Systems, Volume 1; Hardy, Hankel, and Toeplitz An Easy Reading by Nikolai K. Nikolski
  

Operators, Functions, and Systems, Volume 1; Hardy, Hankel, and Toeplitz An Easy Reading

Part of the Mathematical Surveys and Monographs Series

Synopsis

Operators, Functions, and Systems, Volume 1; Hardy, Hankel, and Toeplitz An Easy Reading by Nikolai K. Nikolski

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)

About the Author

Loading other formats...

Book Info

Publication date

15th January 2002

Author

Nikolai K. Nikolski

More books by Nikolai K. Nikolski
Author 'Like for Like'
    recommendations

Publisher

American Mathematical Society

Format

Paperback
461 pages

Categories

Mathematical theory of computation
Differential & Riemannian geometry
Systems analysis & design
Complex analysis, complex variables

ISBN

9780821849330

Lovereading has all the new books and also suggestions for 'similar' authors whilst waiting for your favourites new books.

Carol Peace

It gives a chance to read about new titles, invites comments from all kinds of readers and is run by such a nice bunch of book lovers.

Joy Bosworth

They are bright, breezy and eager to offer a great book, then genuinely listen/respect the review one writes.

Maggie Crane

If you love reading, then you'll love Lovereading! Full of tips & info for every discerning reader.

Lynne Rapson

I love Lovereading because I get to read great books and then get to tell everybody how good they are.

Sally Doel

I read new, exciting writers and established authors before publication and there is a great website full of brilliant books and opinions.

Lynda

It's a lively, independent website with reviews, recommendations and more - with a huge range of books available to buy in all formats.

Alison Layland

I 'Lovereading' because it lets me see what new books are around with a detailed synopsis and readers' reviews.

Judith Sharp

Lovereading4kids

Lovereading4schools