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Birkhäuser - Birkhäuser Mathematics | An Introduction to Frames and Riesz Bases

An Introduction to Frames and Riesz Bases

Christensen, Ole

2003, XXII, 440 p.

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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.

Content Level » Professional/practitioner

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

Related subjects » Birkhäuser Engineering - Birkhäuser Mathematics

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

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