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   -> Volume 6, Issue 8

Book: Interpolation, Identification and Sampling
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J R Partington (

PostPosted: Tue Aug 12, 1997 10:11 am    
Subject: Book: Interpolation, Identification and Sampling
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#1 Book: Interpolation, Identification and Sampling

New Book

Interpolation, Identification and Sampling, by Jonathan R. Partington.

London Mathematical Society Monographs, no. 17, Oxford University
Press, July 1997. xii+267pp. 18 figures. ISBN 0-19-850024-6.

This book presents applications of functional analysis and operator
theory to problems of interpolation of analytic functions, systems
identification, and sampling of signals.

1. Function spaces and operators --- Fourier series and approximate
identities, Fourier and Laplace transforms, Function spaces on the
disc, Function spaces on the half-plane, Blaschke products and zero
sets, Toeplitz and Hankel operators.

2. Interpolation and recovery --- Classical interpolation problems,
Zero sets for the disc algebra, Extension and recovery in the disc
algebra, Totik's recovery theorem, Interpolating sequences.

3. Worst-case identification of functions --- Causal operators and
linear systems, Worst-case identification in the disc algebra,
Two-stage algorithms, Model sets and Chebyshev identification,
Band-limited identification on the circle.

4. Approximation and interpolation --- $n$-widths and approximation,
Hankel-norm approximation, Bases and decompositions in the disc
algebra, IBC and optimal algorithms, Interpolation and validation.

5. Hilbert space methods --- Reproducing kernel Hilbert spaces, The
matching pursuit algorithm, Minimal-norm interpolation, Least squares
methods, Frames and wavelets.

6. Convolution operators --- Worst-case identification of
convolutions, Probabilistic inequalities, Chebyshev identification and
input design, Identification in $ell _2$, IBC and validation.

7. Sampling --- The Paley-Wiener spaces, Regular sampling, General
sampling, Balayage.

8. Applications --- Linear systems, $H_infty$ control, Examples of

Contributed by Jonathan Partington (
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