**Contemporary Mathematics**

Volume: 190;
1995;
354 pp;
Softcover

MSC: Primary 33; 41; 42; 94;

Print ISBN: 978-0-8218-0384-4

Product Code: CONM/190

List Price: $75.00

AMS Member Price: $60.00

MAA Member Price: $67.50

**Electronic ISBN: 978-0-8218-7781-4
Product Code: CONM/190.E**

List Price: $75.00

AMS Member Price: $60.00

MAA Member Price: $67.50

# Mathematical Analysis, Wavelets, and Signal Processing

Share this page *Edited by *
*Mourad E.H. Ismail; M. Zuhair Nashed; Ahmed I. Zayed; Ahmed F. Ghaleb*

This book contains the proceedings of an
international conference held in Cairo, Egypt (January 1994). This
glorious ancient city was the gathering place for mathematicians and
engineers to exchange ideas and to discuss new research trends.

Mathematics and engineering discoveries, such as
wavelets, multiresolution analysis, and subband coding schemes, caused
rapid advancements in signal processing, necessitating an
interdisciplinary approach.

Contributors to this conference demonstrated that some
traditional areas of mathematical analysis—sampling theory,
approximation theory, and orthogonal polynomials—have proven
extremely useful in solving various signal processing problems.

Features P. L. Butzer on…

With several articles discussing the most recent advances and new
trends in mathematical analysis and signal processing, this book
emphasizes interactions between mathematics and electrical
engineering.

#### Readership

Mathematicians, engineers and graduate students in mathematics.

# Table of Contents

## Mathematical Analysis, Wavelets, and Signal Processing

- Contents vii8 free
- Preface ix10 free
- Mathematics in Egypt and its connections with the Court School of Charlemagne 112 free
- Towards a survey of Paul Butzer's contributions to approximation theory 3142
- Ergodic theorems for semigroups and cosine operator functions at zero and infinity with rates and applications to partial differential equations. A survey 6778
- Modular estimates and modular convergence for linear integral operators 95106
- An abstract two-point boundary value problem 107118
- A Riemann–Lebesgue lemma for Jacobi expansions 117128
- Centroids: Fast Fourier transform versus wavelets 127138
- Rapidly converging series representations for zeta-type functions 143154
- Sampling for multi-band functions 165176
- Askey-Wilson operators 171182
- Reducing the Gibbs phenomenon in a Fourier-Bessel series, Hankel and Fourier transforms 179190
- Divergence almost everywhere of a pointwise comparison between convolution processes and their discrete analogues 195206
- Generalized multiresolution analysis and convergence of spline approximations on Rd 209220
- Reproducing kernel Hilbert spaces from sampling expansions 221232
- Sinc convolution—A tool for circumventing some limitations of classical signal processing 227238
- Bounds for the aliasing error in nonuniform sinc interpolation 241252
- The SUP norm of a weighted polynomial: Alternative proof 253264
- A simplified square wave transform for signal processing 265276
- The use of attributed automaton in the recognition of handwritten numerals 273284
- Jacobi polynomials of type BC, Jack polynomials, limit transitions andO(∞) 283294
- The last of the hypergeometric continued fractions 287298
- Processing of FSK/FH signals with unknown code 295306
- A theory of extended pseudo-biorthogonal bases and its application to generalized sampling theorem 305316
- On discrete band-limited signal extrapolation 323334
- Periodic splines and wavelets 339350