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An Introduction to Frames and Riesz Bases (Applied and Numerical Harmonic Analysis)

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An Introduction to Frames and Riesz Bases (Applied and Numerical Harmonic Analysis) Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

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.

Table of Contents

Preface Frames in Finite-dimensional Inner Product Spaces Infinite-dimensional Vector Spaces and Sequences Bases Bases and their Limitations Frames in Hilbert Spaces Frames versus Riesz Bases Frames of Translates Gabor Frames in L2(R) Selected Topics on Gabor Frames Gabor Frames in l2(Z) General Wavelet Frames Dyadic Wavelet Frames Frame Multiresolution Analysis Wavelet Frames via Extension Principles Perturbation of Frames Approximation of the Inverse Frame Operator Expansions in Banach Spaces Appendix List of Symbols References Index

Product Details

ISBN:
9780817642952
Author:
Christensen, Ole
Publisher:
Birkhauser
Author:
Christensen, OLE
Location:
Boston, MA
Subject:
Mathematics
Subject:
Mathematical Analysis
Subject:
Applied
Subject:
Signal processing
Subject:
Vector Analysis
Subject:
Signal processing -- Mathematics.
Subject:
Bases (Linear topological spaces)
Subject:
Mathematics : Vector Analysis
Subject:
Functional Analysis
Subject:
APPLICATIONS OF MATHEMATICS
Subject:
Operator theory
Subject:
Signal, Image and Speech Processing
Subject:
B
Subject:
mathematics and statistics
Copyright:
Edition Number:
1
Edition Description:
Book
Series:
Applied and Numerical Harmonic Analysis
Publication Date:
January 2003
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
464
Dimensions:
235 x 155 mm 1830 gr

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Related Subjects

Science and Mathematics » Environmental Studies » Environment
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An Introduction to Frames and Riesz Bases (Applied and Numerical Harmonic Analysis) New Hardcover
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Product details 464 pages Birkhauser - English 9780817642952 Reviews:
"Synopsis" by , 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.
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