An Introduction to Frames and Riesz Bases - Couverture rigide

Christensen, Ole

Couverture rigide

ISBN 10 : 0817642951 ISBN 13 : 9780817642952

Editeur : Birkhauser Boston Inc, 2002

Synopsis

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.

A propos du livre

Revue de presse

"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

Présentation de l'éditeur

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.

Détails de l'édition

• Éditeur: Birkhauser Boston Inc
• Date d'édition: 2002
• ISBN 10: 0817642951
• ISBN 13: 9780817642952
• Reliure: Relié
• Langue: anglais
• Nombre de pages: 462
• Coordonnées du fabricant: non disponible