Prolate spheroidal wave functions of order zero : mathematical tools for bandlimited approximation
Prolate Spheroidal Wave Functions (PSWFs) are the eigenfunctions of the bandlimited operator in one dimension. As such, they play an important role in signal processing, Fourier analysis, and approximation theory. While historically the numerical evaluation of PSWFs presented serious difficulties, t...
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Livre numérique |
| Lingua: | Anglais |
| Pubblicazione: |
Boston, MA :
Springer US : Imprint: Springer
[20..].
Cham : Springer Nature |
| Serie: | Applied Mathematical Sciences
187 |
| Soggetti: | |
| Accesso online: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Date de publication et éditeur d après le site du fournisseur Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Prolate spheroidal wave functions of order zero, mathematical tools for bandlimited approximation, Andrei Osipov, Vladimir Rokhlin, Hong Xiao, New York, Springer, 2013, 1 vol. (XI-379 p.), Applied mathematical sciences, 978-1-461-48258-1 |
Sommario:
- Introduction Mathematical and Numerical Preliminaries Overview.- Analysis of the Differential Operator.- Analysis of the Integral Operator.- Rational Approximations of PSWFs.-Miscellaneous Properties of PSWFs.- Asymptotic Analysis of PSWFs.- Quadrature Rules and Interpolation via PSWFs.- Numerical Algorithms .-
- 1 Introduction
- 2 Mathematical and Numerical Preliminaries
- 3 Overview
- 4 Analysis of a Differential Operator
- 5 Analysis of the Integral Operator
- 6 Rational Approximations of PSWFs
- 7 Miscellaneous Properties of PSWFs
- 8 Asymptotic Analysis of PSWFs
- 9 Quadrature Rules and Interpolation via PSWFs
- 2.1 Chebyshev Systems
- 2.2 Generalized Gaussian Quadratures
- 2.3 Convolutional Volterra Equations
- 2.4 Prolate Spheroidal Wave Functions
- 2.5 The Dual Nature of PSWFs
- 2.6 Legendre Polynomials and PSWFs
- 2.7 Hermite Polynomials and Hermite Functions
- 2.8 Perturbation of Linear Operators
- 2.9 Elliptic Integrals
- 2.10 Oscillation Properties of Second-Order ODEs
- 2.11 Growth Properties of Second-Order ODEs
- 2.12 Prüfer Transformations
- 2.13 Numerical Tools
- 2.14 Miscellaneous Tools
- 3.1 Relation Between c, n, and n(c)
- 3.2 Relation Between c, n, and n(c)
- 3.3 Properties of PSWFs
- 3.4 PSWF-Based Quadrature Rules
- 4.1 Summary
- 4.2 Oscillation Properties of PSWFs
- 4.3 Growth Properties of PSWFs
- 4.4 Numerical Results
- 5.1 Summary and Discussion
- 5.2 Analytical Tools
- 5.3 Numerical Results
- 6.1 Overview of the Analysis
- 6.2 Oscillation Properties of PSWFs Outside ( 1, 1)
- 6.3 Growth Properties of PSWFs Outside ( 1, 1)
- 6.4 Partial Fraction Expansion of 1/ n
- 6.5 Numerical Results
- 7.1 The Ratio m/ n
- 7.2 Decay of Legendre Coefficients of PSWFs
- 7.3 Additional Properties
- 8.1 Introduction
- 8.2 Analytical Tools
- 8.3 Formulas Based on Legendre Series
- 8.4 Formulas Based on WKB Analysis of the Prolate ODE
- 8.5 Formulas Based on Hermite Series
- 8.6 Numerical Results
- 9.1 Generalized Gaussian Quadrature Rules
- 9.2 Quadrature Rules Based on the Euclidean Algorithm
- 9.3 Interpolation via PSWFs