Authors:
- Fills a gap in the literature: develops frame theory as part of a dialogue between mathematicians and engineers
- Results are presented in a way that is accessible to graduate students in mathematics and engineering
- Extensive exercises are included
- May be used as a textbook in theoretical graduate courses on bases and frames or application-oriented courses focusing on either Gabor anlaysis or wavelets
- For a broad audience of graduate students and researchers in mathematics, mathematical physics, and engineering; also useful for practitioners working in digital signal processing
- Includes supplementary material: sn.pub/extras
Part of the book series: Applied and Numerical Harmonic Analysis (ANHA)
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Table of contents (11 chapters)
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Front Matter
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Back Matter
About this book
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 include results presented in a way that is accessible to graduate students, mathematicians, and engineers; a presentation of 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; and a 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.
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)
Authors and Affiliations
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Inst. Mathematics, Technical University of Denmark, Lyngby, Denmark
Ole Christensen
Bibliographic Information
Book Title: Frames and Bases
Book Subtitle: An Introductory Course
Authors: Ole Christensen
Series Title: Applied and Numerical Harmonic Analysis
DOI: https://doi.org/10.1007/978-0-8176-4678-3
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Boston 2008
Hardcover ISBN: 978-0-8176-4677-6Published: 02 July 2008
eBook ISBN: 978-0-8176-4678-3Published: 05 June 2008
Series ISSN: 2296-5009
Series E-ISSN: 2296-5017
Edition Number: 1
Number of Pages: XVIII, 313
Number of Illustrations: 14 b/w illustrations
Topics: Functional Analysis, Fourier Analysis, Mathematical Modeling and Industrial Mathematics, Signal, Image and Speech Processing, Abstract Harmonic Analysis, Operator Theory