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Applied and Numerical Harmonic Analysis

Frames and Bases

An Introductory Course

Authors: Christensen, Ole

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  • Interdisciplinary approach develops frame theory as part of a dialogue between mathematicians and engineers
  • Extensive exercises make the work suitable as a textbook for use in theoretical graduate courses on bases and frames or application-oriented courses focusing on either Gabor analysis or wavelets
  • Focus on basic topics without too many side remarks makes it easier for students to follow the presentation
  • For a broad audience of graduate students and researchers in pure and applied mathematics, mathematical physics, and engineering, as well as practitioners in digital signal processing
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  • ISBN 978-0-8176-4678-3
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Hardcover $84.99
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About this Textbook

During the last several years, frames have become increasingly popular; they have appeared in a large number of applications, and several concrete constructions of frames of various types have been presented. Most of these constructions were based on quite direct methods rather than the classical sufficient conditions for obtaining a frame. Consequently, there is a need for an updated book on frames, which moves the focus from the classical approach to a more constructive one.

Based on a streamlined presentation of the author's previous work, An Introduction to Frames and Riesz Bases, this new textbook fills a gap in the literature, developing frame theory as part of a dialogue between mathematicians and engineers. Newly added sections on applications will help mathematically oriented readers to see where frames are used in practice and engineers to discover the mathematical background for applications in their field.

Key features and topics:

* Results presented in an accessible way for graduate students, pure and applied mathematicians as well as engineers.

* An introductory chapter provides basic results in finite-dimensional vector spaces, enabling readers with a basic knowledge of linear algebra to understand the idea behind frames without the technical complications in infinite-dimensional spaces.

* Extensive exercises for use in theoretical graduate courses on bases and frames, or applications-oriented courses focusing on either Gabor analysis or wavelets.

* Detailed description of frames with full proofs, an examination of the relationship between frames and Riesz bases, and a discussion of various ways to construct frames.

* Content split naturally into two parts: The first part describes the theory on an abstract level, whereas the second part deals with explicit constructions of frames with applications and connections to time-frequency analysis, Gabor analysis, and wavelets.

Frames and Bases: An Introductory Course will be an excellent textbook for graduate students as well as a good reference for researchers working in pure and applied mathematics, mathematical physics, and engineering. Practitioners working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find the book a useful self-study resource.

Reviews

From the reviews:

"The author’s aim is to present the central ideas of frame and basis theory. … the book is aimed toward graduate students in mathematics, pure and applied mathematicians, and practicing engineers." (William J. Satzer, The Mathematical Association of America, December, 2008)


Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $64.99
price for USA in USD (gross)
  • ISBN 978-0-8176-4678-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $84.99
price for USA in USD
  • ISBN 978-0-8176-4677-6
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Frames and Bases
Book Subtitle
An Introductory Course
Authors
Series Title
Applied and Numerical Harmonic Analysis
Copyright
2008
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-0-8176-4678-3
DOI
10.1007/978-0-8176-4678-3
Hardcover ISBN
978-0-8176-4677-6
Series ISSN
2296-5009
Edition Number
1
Number of Pages
XVIII, 313
Number of Illustrations
14 b/w illustrations
Topics

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