Applied and Numerical Harmonic Analysis

Approximation Theory

From Taylor Polynomials to Wavelets

Authors: Christensen, Ole, Christensen, Khadija Laghrida

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eBook $29.99
price for USA (gross)
  • ISBN 978-0-8176-4448-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.99
price for USA
  • ISBN 978-0-8176-3600-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

About the authors

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

Reviews

"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


Table of contents (5 chapters)

  • Approximation with Polynomials

    Christensen, Ole (et al.)

    Pages 1-14

  • Infinite Series

    Christensen, Ole (et al.)

    Pages 15-50

  • Fourier Analysis

    Christensen, Ole (et al.)

    Pages 51-82

  • Wavelets and Applications

    Christensen, Ole (et al.)

    Pages 83-104

  • Wavelets and their Mathematical Properties

    Christensen, Ole (et al.)

    Pages 105-136

Buy this book

eBook $29.99
price for USA (gross)
  • ISBN 978-0-8176-4448-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.99
price for USA
  • ISBN 978-0-8176-3600-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Approximation Theory
Book Subtitle
From Taylor Polynomials to Wavelets
Authors
Series Title
Applied and Numerical Harmonic Analysis
Copyright
2005
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-0-8176-4448-2
DOI
10.1007/978-0-8176-4448-2
Softcover ISBN
978-0-8176-3600-5
Series ISSN
2296-5009
Edition Number
1
Number of Pages
XI, 156
Number of Illustrations and Tables
5 b/w illustrations
Topics