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Operators, Functions, and Systems, Volume 1; Hardy, Hankel, and Toeplitz - An Easy Reading (Paperback)
Loot Price: R3,213
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Operators, Functions, and Systems, Volume 1; Hardy, Hankel, and Toeplitz - An Easy Reading (Paperback)
Series: Mathematical Surveys and Monographs
Expected to ship within 12 - 19 working days
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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)
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