Authors:
- 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
Part of the book series: Applied and Numerical Harmonic Analysis (ANHA)
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Table of contents (17 chapters)
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Front Matter
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Back Matter
About this book
Reviews
From the reviews:
"The book is well written, the proofs are clear and not too terse, and the work is well suited for use as a textbook. The author has made many contributions to the theory of frames and Riesz bases, and the book benefits from his scope and perspective." —Zentralblatt Math
"The book is a well-written and detailed course into the theory of bases and frames in Hilbert spaces. The composition is very clear, and the proofs are well achieved…. In the basic chapters, a large number of carefully chosen examples and exercises are included. That first part can be used in a graduate course. The material of the later chapters is more in the line of current research…. I recommend this book to graduate students and researchers working in pure and applied mathematics. It will appeal to an audience interested in the theory behind many signal processing tools stimulating further research." —ZAA
"The last decade witnessed a significant change in the field of data representation, with the theory and applications of redundant representations taking center stage and becoming a central research topic in the areas of wavelet and Gabor representations. The specific topic of frame representations received particular attention and became a major theme for these efforts. [This book]…successfully summarizes that progress. Some of its chapters are basic, and are suitable for use in a graduate course in mathematics. Other chapters provide the specialist with a detailed up-to-date review of the state-of-the-art in the field. Other scientists, with more general interest in the area, might use the book as a general reference on the topic." —Journal of Approximation Theory
"This is the first book giving a comprehensive overview over the theory of frames and Riesz basis, which has become important in connection with wavelet theory andnonorthogonal signal expansions. Technically speaking frames in a Hilbert space are the correct analogue of a sequence of generators in a finite-dimensional vector space, while the concept of dual frames corresponds to the notion of pseudo-inverse matrices (widely underestimated in standard courses). The book provides a gentle introduction into the field, is suitable for self-study or for the design of a course, and leads from the beginnings to active research areas. Hence it should be found in any library." —Monatshefte für Mathematik
"Ole Christensen’s An Introduction to Frames and Riesz Bases is a first-rate introduction to the field … . The book provides an excellent exposition of these topics. The material is broad enough to pique the interest of many readers, the included exercises supply some interesting challenges, and the coverage provides enough background for those new to the subject to begin conducting original research." (Eric S. Weber, American Mathematical Monthly, Vol. 112, February, 2005)
Authors and Affiliations
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Department of Mathematics, Technical University of Denmark, Lyngby, Denmark
Ole Christensen
Bibliographic Information
Book Title: An Introduction to Frames and Riesz Bases
Authors: Ole Christensen
Series Title: Applied and Numerical Harmonic Analysis
DOI: https://doi.org/10.1007/978-0-8176-8224-8
Publisher: Birkhäuser Boston, MA
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 2003
Softcover ISBN: 978-1-4612-6500-9Published: 27 November 2013
eBook ISBN: 978-0-8176-8224-8Published: 01 December 2013
Series ISSN: 2296-5009
Series E-ISSN: 2296-5017
Edition Number: 1
Number of Pages: XXII, 440
Topics: Functional Analysis, Applications of Mathematics, Operator Theory, Signal, Image and Speech Processing