An Introduction to Frames and Riesz Bases

  • Ole Christensen

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

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Ole Christensen
    Pages 45-77
  3. Ole Christensen
    Pages 79-86
  4. Ole Christensen
    Pages 87-121
  5. Ole Christensen
    Pages 123-136
  6. Ole Christensen
    Pages 137-165
  7. Ole Christensen
    Pages 167-199
  8. Ole Christensen
    Pages 201-234
  9. Ole Christensen
    Pages 235-248
  10. Ole Christensen
    Pages 249-271
  11. Ole Christensen
    Pages 273-281
  12. Ole Christensen
    Pages 283-311
  13. Ole Christensen
    Pages 313-346
  14. Ole Christensen
    Pages 347-363
  15. Ole Christensen
    Pages 365-382
  16. Ole Christensen
    Pages 383-401
  17. Back Matter
    Pages 403-440

About this book


The theory for frames and bases has developed rapidly in recent years because of its role as a mathematical tool in signal and image processing. In this self-contained work, frames and Riesz bases are presented from a functional analytic point of view, emphasizing their mathematical properties. This is the first comprehensive book to focus on the general properties and interplay of frames and Riesz bases, and thus fills a gap in the literature.
Key features:
* Basic results presented in an accessible way for both pure and applied mathematicians
* Extensive exercises make the work suitable as a textbook for use in graduate courses
* Full proofs included in introductory chapters; only basic knowledge of functional analysis required
* Explicit constructions of frames with applications and connections to time-frequency analysis, wavelets, and nonharmonic Fourier series
* Selected research topics presented with recommendations for more advanced topics and further reading
* Open problems to simulate further research

An Introduction to Frames and Riesz Basis will be of interest to graduate students and researchers working in pure and applied mathematics, mathematical physics, and engineering. Professionals working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find this book a useful self-study reference.


Hilbert space Symbol digital signal processing functional analysis image processing mathematical physics signal processing wavelets

Authors and affiliations

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

Bibliographic information

  • DOI
  • Copyright Information Birkhäuser Boston 2003
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6500-9
  • Online ISBN 978-0-8176-8224-8
  • Series Print ISSN 2296-5009
  • Series Online ISSN 2296-5017
  • Buy this book on publisher's site
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