Prolate Spheroidal Wave Functions of Order Zero Mathematical Tools for Bandlimited Approximation /

• Main Authors: Osipov, Andrei. (Author), Rokhlin, Vladimir. (Author), Xiao, Hong. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Boston, MA : Springer US : Imprint: Springer, 2013.
• Series: Applied Mathematical Sciences, 187
• Subjects: Mathematics.; Numerical analysis.; Engineering mathematics.; Numerical Analysis.; Signal, Image and Speech Processing.; Appl.Mathematics/Computational Methods of Engineering.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-1-4614-8259-8

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...

Table of Contents:

• 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 .-�.