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...
Tallennettuna:
| Päätekijä: | |
|---|---|
| Muut tekijät: | |
| Aineistotyyppi: | Livre numérique |
| Kieli: | Anglais |
| Julkaistu: |
Boston, MA :
Birkhäuser Boston
2005.
Cham : Springer Nature |
| Sarja: | Applied and Numerical Harmonic Analysis
|
| Linkit: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Huomautus: |
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 |
Sisällysluettelo:
- 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