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The Resource A Basis Theory Primer : Expanded Edition, by Christopher Heil, (electronic resource)
A Basis Theory Primer : Expanded Edition, by Christopher Heil, (electronic resource)
Resource Information
The item A Basis Theory Primer : Expanded Edition, by Christopher Heil, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item A Basis Theory Primer : Expanded Edition, by Christopher Heil, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 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 selfcontained 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 timefrequency 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: * Selfcontained 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 learningbydoing, making the text suitable for graduatelevel 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.birkhauserscience.com/9780817646868/. * 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 graduatelevel course. Instructors have several options for building a course around the text depending on the level and background of their students
 Language

 eng
 eng
 Edition
 expanded ed.
 Extent
 1 online resource (548 p.)
 Note
 Description based upon print version of record
 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
 Isbn
 9780817646875
 Label
 A Basis Theory Primer : Expanded Edition
 Title
 A Basis Theory Primer
 Title remainder
 Expanded Edition
 Statement of responsibility
 by Christopher Heil
 Subject

 Applied mathematics
 Engineering mathematics
 Fourier Analysis
 Fourier analysis
 Functional Analysis
 Functional analysis
 Harmonic analysis
 Image processing
 Mathematical and Computational Engineering
 Signal processing
 Signal, Image and Speech Processing
 Speech processing systems
 Abstract Harmonic Analysis
 Applications of Mathematics
 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 selfcontained 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 timefrequency 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: * Selfcontained 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 learningbydoing, making the text suitable for graduatelevel 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.birkhauserscience.com/9780817646868/. * 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 graduatelevel course. Instructors have several options for building a course around the text depending on the level and background of their students
 http://library.link/vocab/creatorName
 Heil, Christopher
 Dewey number
 515.785
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
 I4GtoEs9VjU
 Language note
 English
 LC call number
 QA403403.3
 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)
 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
 10.1007/9780817646875
 Specific material designation
 remote
 System control number

 (CKB)2670000000056830
 (EBL)3066058
 (SSID)ssj0000449069
 (PQKBManifestationID)11309057
 (PQKBTitleCode)TC0000449069
 (PQKBWorkID)10392460
 (PQKB)11778474
 (DEHe213)9780817646875
 (MiAaPQ)EBC3066058
 (EXLCZ)992670000000056830
 Label
 A Basis Theory Primer : Expanded Edition, by Christopher Heil, (electronic resource)
 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
 10.1007/9780817646875
 Specific material designation
 remote
 System control number

 (CKB)2670000000056830
 (EBL)3066058
 (SSID)ssj0000449069
 (PQKBManifestationID)11309057
 (PQKBTitleCode)TC0000449069
 (PQKBWorkID)10392460
 (PQKB)11778474
 (DEHe213)9780817646875
 (MiAaPQ)EBC3066058
 (EXLCZ)992670000000056830
Subject
 Applied mathematics
 Engineering mathematics
 Fourier Analysis
 Fourier analysis
 Functional Analysis
 Functional analysis
 Harmonic analysis
 Image processing
 Mathematical and Computational Engineering
 Signal processing
 Signal, Image and Speech Processing
 Speech processing systems
 Abstract Harmonic Analysis
 Applications of Mathematics
Member of
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History of Science CollectionsBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 97.447906

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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.libraries.ou.edu/portal/ABasisTheoryPrimerExpandedEditionby/hyUmZTdapJ0/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.libraries.ou.edu/portal/ABasisTheoryPrimerExpandedEditionby/hyUmZTdapJ0/">A Basis Theory Primer : Expanded Edition, by Christopher Heil, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.libraries.ou.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.libraries.ou.edu/">University of Oklahoma Libraries</a></span></span></span></span></div>