An Introduction to Frames and Riesz Bases

Ole Christensen

ISBN 10: 1461265002 / ISBN 13: 9781461265009

Published by Springer, Basel, Birkhäuser, 2013

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9781461265009

Bibliographic Details

• Title: An Introduction to Frames and Riesz Bases
• Publisher: Springer, Basel, Birkhäuser
• Publication Date: 2013
• Language: English
• ISBN 10: 1461265002
• ISBN 13: 9781461265009
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 237W x 156H x 25D millimeters 237 millimeters width by 156 millimeters height by 25 millimeters depth
• Weight: 712 grams

About this title

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. This is the first comprehensive book to focus on the general properties and interplay of frames and Riesz bases, emphasizing their mathematical aspects. Rich in exercises, applications, and open problems, the work is aimed at graduate students and researchers in pure and applied mathematics, math physics, and engineering. Minimal prerequisites also make the book accessible to professionals working in digital signal processing who wish to understand the theory behind many modern signal processing tools.

From the Back Cover

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.