Approximation Theory

1. Front Matter

   Pages i-xi

   PDF

2. Approximation with Polynomials

   • Ole Christensen, Khadija L. Christensen

   Pages 1-14

3. Infinite Series

   • Ole Christensen, Khadija L. Christensen

   Pages 15-50

4. Fourier Analysis

   • Ole Christensen, Khadija L. Christensen

   Pages 51-82

5. Wavelets and Applications

   • Ole Christensen, Khadija L. Christensen

   Pages 83-104

6. Wavelets and their Mathematical Properties

   • Ole Christensen, Khadija L. Christensen

   Pages 105-136

7. Back Matter

   Pages 137-156

   PDF

This book gives an elementary introduction to a classical area of mathemat­ ics - approximation theory - in a way that naturally leads to the modern field of wavelets. The main thread throughout the book is the idea of ap­ proximating "complicated expressions" with "simpler expressions," and how this plays a decisive role in many areas of modern mathematics and its applications. One of the main goals of the presentation is to make it clear to the reader that mathematics is a subject in a state of continuous evolution. This fact is usually difficult to explain to students at or near their second year of uni­ versity. Often, teachers do not have adequate elementary material to give to students as motivation and encouragement for their further studies. The present book will be of use in this context because the exposition demon­ strates the dynamic nature of mathematics and how classical disciplines influence many areas of modern mathematics and applications. The book may lead readers toward more advanced literature, such as the other pub­ lications in the Applied and Numerical Harmonic Analysis series (ANHA), by introducing ideas presented in several of those books in an elementary context. The focus here is on ideas rather than on technical details, and the book is not primarily meant to be a textbook.

• Fourier transform
• Haar wavelet
• Symbol
• data compression
• harmonic analysis
• signal analysis
• signal processing

"Approximation methods and wavelets have found many important applications in signal processing. This well-written textbook provides an elementary introduction to approximation theory. The authors concentrate on the presentation of main ideas and demonstrate the great influence of classical approximation theory on modern applied mathematics. This book, with many illustrative examples, is easy to read…[and] will be very useful for anyone interested in approximation theory and wavelets."   —Zentralblatt Math

• Department of Mathematics, Technical University of Denmark, Lyngby, Denmark

  Ole Christensen, Khadija L. Christensen

Ole Christensen is the author of An Introduction to Frames and Riesz Bases (0-8176-4295-1).

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