Approximation Theory : From Taylor Polynomials to Wavelets
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...
保存先:
| 第一著者: | |
|---|---|
| その他の著者: | |
| フォーマット: | Livre numérique |
| 言語: | Anglais |
| 出版事項: |
Boston, MA :
Birkhäuser Boston
2005.
Cham : Springer Nature |
| シリーズ: | Applied and Numerical Harmonic Analysis
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| オンライン･アクセス: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| 注記: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Approximation Theory, Texte imprimé, 9781468495966 • Approximation Theory, From Taylor Polynomials to Wavelets, Ole Christensen, Khadija L. Christensen, Boston, Birkhäuser, 2004, 1 vol. (XI-156 p.), Applied and Numerical Harmonic Analysis, 0-8176-3600-5 |
| LEADER | 05062nam a22003377a 4500 | ||
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| 008 | 180606s2005 xx ||| |||| 00| 0 eng d | ||
| 009 | PPN22740257X | ||
| 020 | |a 9780817644482 | ||
| 041 | 0 | |a eng | |
| 082 | |a 515.2433 | ||
| 100 | 1 | |a Christensen, Ole, |d 1966-...., |c mathématicienne. | |
| 245 | 1 | 0 | |a Approximation Theory : |b From Taylor Polynomials to Wavelets |c by Ole Christensen ; Khadija L. Christensen. |
| 260 | |a Boston, MA : |b Birkhäuser Boston. | ||
| 260 | |a Cham : |b Springer Nature, |c 2005. | ||
| 490 | 0 | |a Applied and Numerical Harmonic Analysis |x 2296-5017 | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 0 | |a 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 | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. chttps://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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. | ||
| 700 | 1 | |a Christensen, Khadija Laghrida. |4 pbd | |
| 776 | 0 | |t Approximation Theory |b Texte imprimé |z 9781468495966 | |
| 776 | 0 | |0 07803924X |t Approximation Theory |o From Taylor Polynomials to Wavelets |f Ole Christensen, Khadija L. Christensen |c Boston |n Birkhäuser |d 2004 |p 1 vol. (XI-156 p.) |s Applied and Numerical Harmonic Analysis |z 0-8176-3600-5 | |
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