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**About this book :- **
**The Gibbs Phenomenon in Fourier Analysis, Splines & Wavelet Approximations ** written by
** Abdul J. Jerri **.

This book represents the first attempt at a unified picture for the presence of the Gibbs (or Gibbs-Wilbraham) phenomenon in applications, its analysis and the different methods of filtering it out. The analysis and filtering cover the familiar Gibbs phenomenon in Fourier series and integral representations of functions with jump discontinuities. In addition it will include other representations, such as general orthogonal series expansions, general integral transforms, splines approximation, and continuous as well as discrete wavelet approximations. The material in this book is presented in a manner accessible to upperclassmen and graduate students in science and engineering, as well as researchers who may face the Gibbs phenomenon in the varied applications that involve the Fourier and the other approximations of functions with jump discontinuities. Those with more advanced backgrounds in analysis will find basic material, results, and motivations from which they can begin to develop deeper and more general results. We must emphasize that the aim of this book (the first on the sUbject): to satisfy such a diverse audience, is quite difficult. In particular, our detailed derivations and their illustrations for an introductory book may very well sound repetitive to the experts in the field who are expecting a research monograph. To answer the concern of the researchers, we can only hope that this book will prove helpful as a basic reference for their research papers.

In addition, there is always the possibility of following it by a research monograph. To accommodate all those concerned with emphasis on the clarity with some intuition, we shall quote only the very basic theorems, such as those of Fourier and wavelet analysis. The basic and most likely familiar results and theorems of Fourier analysis are reviewed in Chapter 1. We will rely on a good number of the basic references that date back to Wilbraham in 1848. For completeness, we are also including most other references that deal with the Gibbs phenomenon in some way or another. They are placed separately as "Other Related References" in an Appendix following the main bibliography of this book. To distinguish these references from the ones used in the text, we have added aprefix A to their (separate) numbers. These references also include some very recent ones, or few "somewhat" relevant ones, that were discovered too late to be included in our general discussion. For completeness, we shall list such references at the end of their corresponding sections.

(Abdul J. Jerri)

**Book Detail :- **
** Title: ** The Gibbs Phenomenon in Fourier Analysis, Splines & Wavelet Approximations
** Edition: **
** Author(s): ** Abdul J. Jerri
** Publisher: ** Springer US
** Series: ** Mathematics and Its Applications 446
** Year: ** 1998
** Pages: ** 356
** Type: ** PDF
** Language: ** English
** ISBN: ** 978-1-4419-4800-7,978-1-4757-2847-7
** Country: ** US
**Download Similar Books from Amazon **

**About Author :- **

The author **Abdul Jabbar Hassoon Jerri** is an Iraqi American mathematician, most recognized for his contributions to Shannon Sampling Theory, It's Generalizations, Error Analysis, and Historical Reviews, and in particular his establishment in 2002 of the journal Sampling Theory in Signal and Image Processing (STSIP-ISSN 1530-6429) with over thirty top international experts as its editors, besides establishing its Sampling Publishing, also his contribution to the general understanding of the Gibbs Phenomenon, where he wrote the first book ever on the subject, published by Springer - Verlag, then he followed it by editing another book on Advances in Gibbs Phenomenon published by Sampling Publishing.

Abdul Jerri earned a B.Sc. in Physics with honors at the University of Baghdad (1955) and M.S. in Physics from Illinois Institute of Technology (1960) in Chicago where he continued to work within the research group (1960–63) in Reactor Physics and Radiation streaming in Shelter Entrance ways. He also earned a Ph.D. in Mathematics from Oregon State University in 1967 with the dissertation title On Extensions of the Generalized Sampling Theorem.

Abdul Jerri commenced his tenure with the faculty of the Department of Mathematics and Computer Science at Clarkson University in Potsdam, NY (1967), where he worked from 1967 until his retirement as Professor Emeritus in 2002.

Abdul Jerri's career includes visiting positions at the American University in Cairo, where he established the Study Programs in Mathematics and Computer Science (1972–74). He was also the Director of the Graduate Mathematics Study Program at Kuwait University (1978–80).

He is the author of several other popular books: Introduction to Integral Equations with Applications, accompanied by a Students Solution Manual: Sampling Publishing,Introduction to Wavelets accompanied by a Students Solution Manual( The latter Manual was co-authored with Prof Masaru Kamada); Sampling Publishing. Other books include Integral and Discrete Transforms with Applications and Error Analysis: Marcel Dekker, and Linear Difference Equations with Discrete Transform Methods:Sp ringer-Verlag.

He had published over forty papers, with numerous lectures on his areas of research interest nationally and internationally. Jerri's main research interests include the areas of Integral and Discrete Transforms, Sampling Expansion and its Applications,History and Error Analysis, the Gibbs Phenomenon, Transform-Iterative Methods for Nonlinear Problems, and Operational Sum Methods for Difference Equations.

In his first workshop, he introduced the subject of Shannon Sampling Theory in four-one hour lectures. In 1997 workshop in Aveiro, Portugal, the Proceedings of the workshop was dedicated to jerri 65th birthday. Presently, he is working on writing a Tutorial review paper on the subject "Multidimensional sampling in Signal Processing. He is dedicating this paper for the occasion of the CENTENNIAL of the American Scientist of the century, the father of Information Theory, Claude Elwood Shannon.

**All Famous Books of this Author :- **

Here is list all books, text books, editions, versions, solution manuals or solved notes avaliable of this author, We recomended you to download all.

** • Read Online Introduction to Integral Equations with Applications by Abdul Jerri **

** • Download PDF Integral & Discrete Transforms with Applications & Error Analysis by Abdul Jerri **

** • Download PDF Linear Difference Equations with Discrete Transform Methods by Abdul J. Jerri **

** • Download PDF The Gibbs Phenomenon in Fourier Analysis, Splines & Wavelet Approximations by Abdul J. Jerri **

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**Book Contents :- **
**The Gibbs Phenomenon in Fourier Analysis, Splines & Wavelet Approximations ** written by
** Abdul J. Jerri **
cover the following topics.

Preface

ACKNOWLEDGEMENTS

AIM OF THE BOOK

1. INTRODUCTION

2. ANALYSIS AND FILTERING

3. THE GENERAL ORTHOGONAL EXPANSIONS

4. SPLINES AND OTHER APPROXIMATIONS

5. THE WAVELET REPRESENTATIONS

REFERENCES

Appendix

INDEX OF NOTATIONS

SUBJECT INDEX

AUTHOR INDEX

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