The Resource Approximation Theory : From Taylor Polynomials to Wavelets, by Ole Christensen, Khadija Laghrida Christensen, (electronic resource)

Approximation Theory : From Taylor Polynomials to Wavelets, by Ole Christensen, Khadija Laghrida Christensen, (electronic resource)

Label
Approximation Theory : From Taylor Polynomials to Wavelets
Title
Approximation Theory
Title remainder
From Taylor Polynomials to Wavelets
Statement of responsibility
by Ole Christensen, Khadija Laghrida Christensen
Creator
Contributor
Author
Author
Subject
Language
  • eng
  • eng
Summary
This concisely written book gives an elementary introduction to a classical area of mathematics—approximation theory—in a way that naturally leads to the modern field of wavelets. The exposition, driven by ideas rather than technical details and proofs, demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications. Key features and topics: * Description of wavelets in words rather than mathematical symbols * Elementary introduction to approximation using polynomials (Weierstrass’ and Taylor’s theorems) * Introduction to infinite series, with emphasis on approximation-theoretic aspects * Introduction to Fourier analysis * Numerous classical, illustrative examples and constructions * Discussion of the role of wavelets in digital signal processing and data compression, such as the FBI’s use of wavelets to store fingerprints * Minimal prerequisites: elementary calculus * Exercises that may be used in undergraduate and graduate courses on infinite series and Fourier series Approximation Theory: From Taylor Polynomials to Wavelets will be an excellent textbook or self-study reference for students and instructors in pure and applied mathematics, mathematical physics, and engineering. Readers will find motivation and background material pointing toward advanced literature and research topics in pure and applied harmonic analysis and related areas
Member of
http://library.link/vocab/creatorName
Christensen, Ole
Dewey number
511/.4
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • Huz9oyahSA0
  • UY7d3rUZkFU
Language note
English
LC call number
QA403.5-404.5
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Christensen, Khadija Laghrida.
Series statement
  • Applied and numerical harmonic analysis
  • Applied and Numerical Harmonic Analysis,
http://library.link/vocab/subjectName
  • Fourier analysis
  • Mathematics
  • Harmonic analysis
  • Functional analysis
  • Fourier Analysis
  • Approximations and Expansions
  • Abstract Harmonic Analysis
  • Functional Analysis
  • Applications of Mathematics
  • Signal, Image and Speech Processing
Label
Approximation Theory : From Taylor Polynomials to Wavelets, by Ole Christensen, Khadija Laghrida Christensen, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. [153]-154) and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
1 Approximation with Polynomials -- 1.1 Approximation of a function on an interval -- 1.2 Weierstrass’ theorem -- 1.3 Taylor’s theorem -- 1.4 Exercises -- 2 Infinite Series -- 2.1 Infinite series of numbers -- 2.2 Estimating the sum of an infinite series -- 2.3 Geometric series -- 2.4 Power series -- 2.5 General infinite sums of functions -- 2.6 Uniform convergence -- 2.7 Signal transmission -- 2.8 Exercises -- 3 Fourier Analysis -- 3.1 Fourier series -- 3.2 Fourier’s theorem and approximation -- 3.3 Fourier series and signal analysis -- 3.4 Fourier series and Hilbert spaces -- 3.5 Fourier series in complex form -- 3.6 Parseval’s theorem -- 3.7 Regularity and decay of the Fourier coefficients -- 3.8 Best N-term approximation -- 3.9 The Fourier transform -- 3.10 Exercises -- 4 Wavelets and Applications -- 4.1 About wavelet systems -- 4.2 Wavelets and signal processing -- 4.3 Wavelets and fingerprints -- 4.4 Wavelet packets -- 4.5 Alternatives to wavelets: Gabor systems -- 4.6 Exercises -- 5 Wavelets and their Mathematical Properties -- 5.1 Wavelets and L2 (?) -- 5.2 Multiresolution analysis -- 5.3 The role of the Fourier transform -- 5.4 The Haar wavelet -- 5.5 The role of compact support -- 5.6 Wavelets and singularities -- 5.7 Best N-term approximation -- 5.8 Frames -- 5.9 Gabor systems -- 5.10 Exercises -- Appendix A -- A.1 Definitions and notation -- A.2 Proof of Weierstrass’ theorem -- A.3 Proof of Taylor’s theorem -- A.4 Infinite series -- A.5 Proof of Theorem 3 7 2 -- Appendix B -- B.1 Power series -- B.2 Fourier series for 2?-periodic functions -- List of Symbols -- References
Dimensions
unknown
Edition
1st ed. 2005.
Extent
1 online resource (165 p.)
Form of item
online
Isbn
9780817644482
Media category
computer
Media type code
  • c
Other control number
10.1007/978-0-8176-4448-2
Specific material designation
remote
System control number
  • (CKB)2670000000276765
  • (EBL)3068768
  • (SSID)ssj0000755051
  • (PQKBManifestationID)11399439
  • (PQKBTitleCode)TC0000755051
  • (PQKBWorkID)10729495
  • (PQKB)11789492
  • (DE-He213)978-0-8176-4448-2
  • (MiAaPQ)EBC3068768
  • (EXLCZ)992670000000276765
Label
Approximation Theory : From Taylor Polynomials to Wavelets, by Ole Christensen, Khadija Laghrida Christensen, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. [153]-154) and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
1 Approximation with Polynomials -- 1.1 Approximation of a function on an interval -- 1.2 Weierstrass’ theorem -- 1.3 Taylor’s theorem -- 1.4 Exercises -- 2 Infinite Series -- 2.1 Infinite series of numbers -- 2.2 Estimating the sum of an infinite series -- 2.3 Geometric series -- 2.4 Power series -- 2.5 General infinite sums of functions -- 2.6 Uniform convergence -- 2.7 Signal transmission -- 2.8 Exercises -- 3 Fourier Analysis -- 3.1 Fourier series -- 3.2 Fourier’s theorem and approximation -- 3.3 Fourier series and signal analysis -- 3.4 Fourier series and Hilbert spaces -- 3.5 Fourier series in complex form -- 3.6 Parseval’s theorem -- 3.7 Regularity and decay of the Fourier coefficients -- 3.8 Best N-term approximation -- 3.9 The Fourier transform -- 3.10 Exercises -- 4 Wavelets and Applications -- 4.1 About wavelet systems -- 4.2 Wavelets and signal processing -- 4.3 Wavelets and fingerprints -- 4.4 Wavelet packets -- 4.5 Alternatives to wavelets: Gabor systems -- 4.6 Exercises -- 5 Wavelets and their Mathematical Properties -- 5.1 Wavelets and L2 (?) -- 5.2 Multiresolution analysis -- 5.3 The role of the Fourier transform -- 5.4 The Haar wavelet -- 5.5 The role of compact support -- 5.6 Wavelets and singularities -- 5.7 Best N-term approximation -- 5.8 Frames -- 5.9 Gabor systems -- 5.10 Exercises -- Appendix A -- A.1 Definitions and notation -- A.2 Proof of Weierstrass’ theorem -- A.3 Proof of Taylor’s theorem -- A.4 Infinite series -- A.5 Proof of Theorem 3 7 2 -- Appendix B -- B.1 Power series -- B.2 Fourier series for 2?-periodic functions -- List of Symbols -- References
Dimensions
unknown
Edition
1st ed. 2005.
Extent
1 online resource (165 p.)
Form of item
online
Isbn
9780817644482
Media category
computer
Media type code
  • c
Other control number
10.1007/978-0-8176-4448-2
Specific material designation
remote
System control number
  • (CKB)2670000000276765
  • (EBL)3068768
  • (SSID)ssj0000755051
  • (PQKBManifestationID)11399439
  • (PQKBTitleCode)TC0000755051
  • (PQKBWorkID)10729495
  • (PQKB)11789492
  • (DE-He213)978-0-8176-4448-2
  • (MiAaPQ)EBC3068768
  • (EXLCZ)992670000000276765

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