Approximation Theory

From Taylor Polynomials to Wavelets

  • Ole Christensen
  • Khadija L. Christensen

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Ole Christensen, Khadija L. Christensen
    Pages 1-14
  3. Ole Christensen, Khadija L. Christensen
    Pages 15-50
  4. Ole Christensen, Khadija L. Christensen
    Pages 51-82
  5. Ole Christensen, Khadija L. Christensen
    Pages 83-104
  6. Ole Christensen, Khadija L. Christensen
    Pages 105-136
  7. Back Matter
    Pages 137-156

About this book

Introduction

This concisely written book gives an elementary introduction to a classical area of mathematics—approximation theory—in a way that naturally leads to the modern field of wavelets. The exposition, driven by ideas rather than technical details and proofs, demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications.

Key features and topics:

* Description of wavelets in words rather than mathematical symbols

* Elementary introduction to approximation using polynomials (Weierstrass’ and Taylor’s theorems)

* Introduction to infinite series, with emphasis on approximation-theoretic aspects

* Introduction to Fourier analysis

* Numerous classical, illustrative examples and constructions

* Discussion of the role of wavelets in digital signal processing and data compression, such as the FBI’s use of wavelets to store fingerprints

* Minimal prerequisites: elementary calculus

* Exercises that may be used in undergraduate and graduate courses on infinite series and Fourier series

Approximation Theory: From Taylor Polynomials to Wavelets will be an excellent textbook or self-study reference for students and instructors in pure and applied mathematics, mathematical physics, and engineering. Readers will find motivation and background material pointing toward advanced literature and research topics in pure and applied harmonic analysis and related areas.

Keywords

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

Authors and affiliations

  • Ole Christensen
    • 1
  • Khadija L. Christensen
    • 1
  1. 1.Department of MathematicsTechnical University of DenmarkLyngbyDenmark

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-4448-2
  • Copyright Information Birkhäuser Boston 2005
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-3600-5
  • Online ISBN 978-0-8176-4448-2
  • About this book