The Resource Frames and Bases : An Introductory Course, by Ole Christensen, (electronic resource)

Frames and Bases : An Introductory Course, by Ole Christensen, (electronic resource)

Label
Frames and Bases : An Introductory Course
Title
Frames and Bases
Title remainder
An Introductory Course
Statement of responsibility
by Ole Christensen
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
During the last several years, frames have become increasingly popular; they have appeared in a large number of applications, and several concrete constructions of frames of various types have been presented. Most of these constructions were based on quite direct methods rather than the classical sufficient conditions for obtaining a frame. Consequently, there is a need for an updated book on frames, which moves the focus from the classical approach to a more constructive one. Based on a streamlined presentation of the author's previous work, An Introduction to Frames and Riesz Bases, this new textbook fills a gap in the literature, developing frame theory as part of a dialogue between mathematicians and engineers. Newly added sections on applications will help mathematically oriented readers to see where frames are used in practice and engineers to discover the mathematical background for applications in their field. Key features and topics: * Results presented in an accessible way for graduate students, pure and applied mathematicians as well as engineers. * An introductory chapter provides basic results in finite-dimensional vector spaces, enabling readers with a basic knowledge of linear algebra to understand the idea behind frames without the technical complications in infinite-dimensional spaces. * Extensive exercises for use in theoretical graduate courses on bases and frames, or applications-oriented courses focusing on either Gabor analysis or wavelets. * Detailed description of frames with full proofs, an examination of the relationship between frames and Riesz bases, and a discussion of various ways to construct frames. * Content split naturally into two parts: The first part describes the theory on an abstract level, whereas the second part deals with explicit constructions of frames with applications and connections to time-frequency analysis, Gabor analysis, and wavelets. Frames and Bases: An Introductory Course will be an excellent textbook for graduate students as well as a good reference for researchers working in pure and applied mathematics, mathematical physics, and engineering. Practitioners working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find the book a useful self-study resource
Member of
http://library.link/vocab/creatorName
Christensen, Ole
Dewey number
  • 515.63
  • 515/.63
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
Huz9oyahSA0
Language note
English
LC call number
QA319-329.9
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Applied and Numerical Harmonic Analysis,
http://library.link/vocab/subjectName
  • Functional analysis
  • Fourier analysis
  • Harmonic analysis
  • Operator theory
  • Functional Analysis
  • Fourier Analysis
  • Mathematical Modeling and Industrial Mathematics
  • Signal, Image and Speech Processing
  • Abstract Harmonic Analysis
  • Operator Theory
Label
Frames and Bases : An Introductory Course, by Ole Christensen, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. [307]-310) and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
Frames in Finite-dimensional Inner Product Spaces -- Infinite-dimensional Vector Spaces and Sequences -- Bases -- Bases and their Limitations -- Frames in Hilbert Spaces -- B-splines -- Frames of Translates -- Shift-Invariant Systems -- Gabor Frames in L(R) -- Gabor Frames in l(Z) -- Wavelet Frames in L(R)
Dimensions
unknown
Edition
1st ed. 2008.
Extent
1 online resource (325 p.)
Form of item
online
Isbn
9780817646783
Media category
computer
Media type code
  • c
Other control number
10.1007/978-0-8176-4678-3
Specific material designation
remote
System control number
  • (CKB)1000000000440901
  • (EBL)371876
  • (OCoLC)272306849
  • (SSID)ssj0000157825
  • (PQKBManifestationID)11182082
  • (PQKBTitleCode)TC0000157825
  • (PQKBWorkID)10139812
  • (PQKB)11335202
  • (DE-He213)978-0-8176-4678-3
  • (MiAaPQ)EBC371876
  • (EXLCZ)991000000000440901
Label
Frames and Bases : An Introductory Course, by Ole Christensen, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. [307]-310) and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
Frames in Finite-dimensional Inner Product Spaces -- Infinite-dimensional Vector Spaces and Sequences -- Bases -- Bases and their Limitations -- Frames in Hilbert Spaces -- B-splines -- Frames of Translates -- Shift-Invariant Systems -- Gabor Frames in L(R) -- Gabor Frames in l(Z) -- Wavelet Frames in L(R)
Dimensions
unknown
Edition
1st ed. 2008.
Extent
1 online resource (325 p.)
Form of item
online
Isbn
9780817646783
Media category
computer
Media type code
  • c
Other control number
10.1007/978-0-8176-4678-3
Specific material designation
remote
System control number
  • (CKB)1000000000440901
  • (EBL)371876
  • (OCoLC)272306849
  • (SSID)ssj0000157825
  • (PQKBManifestationID)11182082
  • (PQKBTitleCode)TC0000157825
  • (PQKBWorkID)10139812
  • (PQKB)11335202
  • (DE-He213)978-0-8176-4678-3
  • (MiAaPQ)EBC371876
  • (EXLCZ)991000000000440901

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