عنوان

An Introduction to Frames and Riesz Bases

(Number (ISBN

9781461265009

(Number (ISMN

10.1007/978-3-319-25613-9

Number

۲۰۱۱۰۱۹۸

System Control Number

(DE-He213)978-3-319-25613-9

.Language of Text, Soundtrack etc

انگلیسی

Title Proper

An Introduction to Frames and Riesz Bases

General Material Designation

[book]

First Statement of Responsibility

/by Ole Christensen.

Place of Publication, Distribution, etc.

Cham

Name of Publisher, Distributor, etc.

.Imprint: Birkhäuser

Date of Publication, Distribution, etc.

,2002

Specific Material Designation and Extent of Item

XIX, 439 p.

Dimensions

;28 cm

Series Title

Applied and Numerical Harmonic Analysis,

ISSN of Series

2296-5009

Text of Note

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 .

International Standard Book Number

9783319256115

International Standard Book Number

9783319256122

International Standard Book Number

9783319798141

Entry Element

Functional analysis.

Entry Element

Harmonic analysis.

Entry Element

Operator theory.

Entry Element

Signal processing.

Entry Element

Image processing.

Entry Element

Speech processing systems.

Entry Element

Functional Analysis.

Entry Element

Abstract Harmonic Analysis.

Entry Element

Operator Theory.

Entry Element

Signal, Image and Speech Processing.

Subject Category Subdivision Code

PBKF

Subject Category Subdivision Code

MAT037000

Subject Category Subdivision Code

PBKF

System Code

bicssc

System Code

bisacsh

System Code

thema

Class number

Book number

Entry Element

Christensen, Ole.

Country

ایران

Agency

Central Library of the Kurdistan University

Date of Transaction

20220129103336.0

Cataloguing Rules (Descriptive Conventions))

rda

p

BL

270410

Y