An Introduction to Frames and Riesz Bases

Ole Christensen

ISBN 10: 3319256114 / ISBN 13: 9783319256115

Published by Birkhäuser, Springer, 2016

About this Item

Druck auf Anfrage Neuware - Printed after ordering - This revised and expanded monograph presents the general theory for frames and Riesz bases in Hilbert spaces as well as its concrete realizations within Gabor analysis, wavelet analysis, and generalized shift-invariant systems. Compared with the first edition, more emphasis is put on explicit constructions with attractive properties. Based on the exiting development of frame theory over the last decade, this second edition now includes new sections on the rapidly growing fields of LCA groups, generalized shift-invariant systems, duality theory for as well Gabor frames as wavelet frames, and open problems in the field. Key features include:\*Elementary introduction to frame theory in finite-dimensional spaces \* 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 and dual pairs of frames, with applications and connections to time-frequency analysis, wavelets, and generalized shift-invariant systems\* Discussion of frames on LCA groups and the concrete realizations in terms of Gabor systems on the elementary groups; connections to sampling theory \* Selected research topics presented with recommendations for more advanced topics and further reading\* Open problems to stimulate further research An Introduction to Frames and Riesz Bases 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. Review of the first edition:'Ole Christensen's An Introduction to Frames and Riesz Bases is a first-rate introduction to the field . . The book provides an excellent exposition of these topics. The material is broad enough to pique the interest of many readers, the included exercises supply some interesting challenges, and the coverage provides enough background for those new to the subject to begin conducting original research.' - Eric S. Weber, American Mathematical Monthly, Vol. 112, February, 2005.

Seller Inventory # 9783319256115

Bibliographic Details

• Title: An Introduction to Frames and Riesz Bases
• Publisher: Birkhäuser, Springer
• Publication Date: 2016
• Language: English
• ISBN 10: 3319256114
• ISBN 13: 9783319256115
• Binding: Buch
• Edition: 2nd Edition
• Condition: Neu
• Dimensions: 241W x 160H x 45D millimeters 241 millimeters width by 160 millimeters height by 45 millimeters depth
• Weight: 1250 grams

About this title

Synopsis

This revised and expanded monograph presents the general theory for frames and Riesz bases in Hilbert spaces as well as its concrete realizations within Gabor analysis, wavelet analysis, and generalized shift-invariant systems.  Compared with the first edition, more emphasis is put on explicit constructions with attractive properties.  Based on the exiting development of frame theory over the last decade, this second edition now includes new sections on the rapidly growing fields of LCA groups, generalized shift-invariant systems, duality theory for as well Gabor frames as wavelet frames, and open problems in the field.

 

Key features include:

*Elementary introduction to frame theory in finite-dimensional spaces
* 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 includ

ed in introductory chapters; only basic knowledge of functional analysis required
* Explicit constructions of frames and dual pairs of frames, with applications and connections to time-frequency analysis, wavelets, and generalized shift-invariant systems

* Discussion of frames on LCA groups and the concrete realizations in terms of Gabor systems on the elementary groups; connections to sampling theory

 * Selected research topics presented with recommendations for more advanced topics and further readin

g

* Open problems to stimulate further research

 

An Introduction to Frames and Riesz Bases 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.

 

Review of the first edition:

"Ole Christensen’s An Introduction to Frames and Riesz Bases is a first-rate introduction to the field … . The book provides an excellent exposition of these topics. The material is broad enough to pique the interest of many readers, the included exercises supply some interesting challenges, and the coverage provides enough background for those new to the subject to begin conducting original research." 

 ― Eric S. Weber, American Mathematical Monthly, Vol. 112, February, 2005 

About the Author

Ole Christensen is a Professor at Technical University of Denmark in the Department of Applied Mathematics and Computer Science. His research interests include harmonic analysis, frame expansions, wavelets, and Gabor systems.