An Introduction to Frames and Riesz Bases

(Autor)

Buch | Hardcover
462 Seiten
2002 | 2003 ed.
Birkhauser Boston Inc (Verlag)
978-0-8176-4295-2 (ISBN)

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An Introduction to Frames and Riesz Bases - Ole Christensen
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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. This title features frames and Riesz bases that are presented from a functional analytic point of view, emphasizing their mathematical properties.
The Applied and Numerical Harmonic Analysis ( ANHA) book series aims to provide the engineering, mathematical, and scientific communities with significant developments in harmonic analysis, ranging from abstract har- monic analysis to basic applications. The title of the series reflects the im- portance of applications and numerical implementation, but richness and relevance of applications and implementation depend fundamentally on the structure and depth of theoretical underpinnings. Thus, from our point of view, the interleaving of theory and applications and their creative symbi- otic evolution is axiomatic. Harmonic analysis is a wellspring of ideas and applicability that has flour- ished, developed, and deepened over time within many disciplines and by means of creative cross-fertilization with diverse areas. The intricate and fundamental relationship between harmonic analysis and fields such as sig- nal processing, partial differential equations (PDEs), and image processing is reflected in our state of the art ANHA series.
Our vision of modern harmonic analysis includes mathematical areas such as wavelet theory, Banach algebras, classical Fourier analysis, time- frequency analysis, and fractal geometry, as well as the diverse topics that impinge on them.

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

Erscheint lt. Verlag 13.12.2002
Reihe/Serie Applied and Numerical Harmonic Analysis
Zusatzinfo biography
Verlagsort Secaucus
Sprache englisch
Maße 156 x 234 mm
Gewicht 829 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Angewandte Mathematik
ISBN-10 0-8176-4295-1 / 0817642951
ISBN-13 978-0-8176-4295-2 / 9780817642952
Zustand Neuware
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