The Resource A Basis Theory Primer : Expanded Edition, by Christopher Heil, (electronic resource)

A Basis Theory Primer : Expanded Edition, by Christopher Heil, (electronic resource)

Label
A Basis Theory Primer : Expanded Edition
Title
A Basis Theory Primer
Title remainder
Expanded Edition
Statement of responsibility
by Christopher Heil
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
The classical subject of bases in Banach spaces has taken on a new life in the modern development of applied harmonic analysis. This textbook is a self-contained introduction to the abstract theory of bases and redundant frame expansions and its use in both applied and classical harmonic analysis. The four parts of the text take the reader from classical functional analysis and basis theory to modern time-frequency and wavelet theory. * Part I develops the functional analysis that underlies most of the concepts presented in the later parts of the text. * Part II presents the abstract theory of bases and frames in Banach and Hilbert spaces, including the classical topics of convergence, Schauder bases, biorthogonal systems, and unconditional bases, followed by the more recent topics of Riesz bases and frames in Hilbert spaces. * Part III relates bases and frames to applied harmonic analysis, including sampling theory, Gabor analysis, and wavelet theory. * Part IV deals with classical harmonic analysis and Fourier series, emphasizing the role played by bases, which is a different viewpoint from that taken in most discussions of Fourier series. Key features: * Self-contained presentation with clear proofs accessible to graduate students, pure and applied mathematicians, and engineers interested in the mathematical underpinnings of applications. * Extensive exercises complement the text and provide opportunities for learning-by-doing, making the text suitable for graduate-level courses; hints for selected exercises are included at the end of the book. * A separate solutions manual is available for instructors upon request at: www.birkhauser-science.com/978-0-8176-4686-8/. * No other text develops the ties between classical basis theory and its modern uses in applied harmonic analysis. A Basis Theory Primer is suitable for independent study or as the basis for a graduate-level course. Instructors have several options for building a course around the text depending on the level and background of their students
Member of
http://library.link/vocab/creatorName
Heil, Christopher
Dewey number
515.785
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
I4GtoEs9VjU
Language note
English
LC call number
QA403-403.3
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Applied and Numerical Harmonic Analysis,
http://library.link/vocab/subjectName
  • Harmonic analysis
  • Applied mathematics
  • Engineering mathematics
  • Functional analysis
  • Fourier analysis
  • Signal processing
  • Image processing
  • Speech processing systems
  • Abstract Harmonic Analysis
  • Mathematical and Computational Engineering
  • Functional Analysis
  • Fourier Analysis
  • Applications of Mathematics
  • Signal, Image and Speech Processing
Label
A Basis Theory Primer : Expanded Edition, by Christopher Heil, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. [515]-526) and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
ANHA Series Preface -- Preface -- General Notation -- Part I. A Primer on Functional Analysis -- Banach Spaces and Operator Theory -- Functional Analysis -- Part II. Bases and Frames -- Unconditional Convergence of Series in Banach and Hilbert Spaces -- Bases in Banach Spaces -- Biorthogonality, Minimality, and More About Bases -- Unconditional Bases in Banach Spaces -- Bessel Sequences and Bases in Hilbert Spaces -- Frames in Hilbert Spaces -- Part III. Bases and Frames in Applied Harmonic Analysis -- The Fourier Transform on the Real Line -- Sampling, Weighted Exponentials, and Translations -- Gabor Bases and Frames -- Wavelet Bases and Frames -- Part IV. Fourier Series -- Fourier Series -- Basic Properties of Fourier Series -- Part V. Appendices -- Lebesgue Measure and Integration -- Compact and Hilbert–Schmidt Operators -- Hints for Exercises -- Index of Symbols -- References -- Index
Dimensions
unknown
Edition
expanded ed.
Extent
1 online resource (548 p.)
Form of item
online
Isbn
9780817646875
Media category
computer
Media type code
  • c
Other control number
10.1007/978-0-8176-4687-5
Specific material designation
remote
System control number
  • (CKB)2670000000056830
  • (EBL)3066058
  • (SSID)ssj0000449069
  • (PQKBManifestationID)11309057
  • (PQKBTitleCode)TC0000449069
  • (PQKBWorkID)10392460
  • (PQKB)11778474
  • (DE-He213)978-0-8176-4687-5
  • (MiAaPQ)EBC3066058
  • (EXLCZ)992670000000056830
Label
A Basis Theory Primer : Expanded Edition, by Christopher Heil, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. [515]-526) and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
ANHA Series Preface -- Preface -- General Notation -- Part I. A Primer on Functional Analysis -- Banach Spaces and Operator Theory -- Functional Analysis -- Part II. Bases and Frames -- Unconditional Convergence of Series in Banach and Hilbert Spaces -- Bases in Banach Spaces -- Biorthogonality, Minimality, and More About Bases -- Unconditional Bases in Banach Spaces -- Bessel Sequences and Bases in Hilbert Spaces -- Frames in Hilbert Spaces -- Part III. Bases and Frames in Applied Harmonic Analysis -- The Fourier Transform on the Real Line -- Sampling, Weighted Exponentials, and Translations -- Gabor Bases and Frames -- Wavelet Bases and Frames -- Part IV. Fourier Series -- Fourier Series -- Basic Properties of Fourier Series -- Part V. Appendices -- Lebesgue Measure and Integration -- Compact and Hilbert–Schmidt Operators -- Hints for Exercises -- Index of Symbols -- References -- Index
Dimensions
unknown
Edition
expanded ed.
Extent
1 online resource (548 p.)
Form of item
online
Isbn
9780817646875
Media category
computer
Media type code
  • c
Other control number
10.1007/978-0-8176-4687-5
Specific material designation
remote
System control number
  • (CKB)2670000000056830
  • (EBL)3066058
  • (SSID)ssj0000449069
  • (PQKBManifestationID)11309057
  • (PQKBTitleCode)TC0000449069
  • (PQKBWorkID)10392460
  • (PQKB)11778474
  • (DE-He213)978-0-8176-4687-5
  • (MiAaPQ)EBC3066058
  • (EXLCZ)992670000000056830

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