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On Spectral Approximations by Generalized Slepian Functions

Published online by Cambridge University Press:  28 May 2015

Jing Zhang and
Li-Lian Wang
Jing Zhang
Affiliation:
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
Li-Lian Wang*
Affiliation:
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
*
Corresponding author.Email address:lilian@ntu.edu.sg
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Abstract

We introduce a family of orthogonal functions, termed as generalized Slepian functions (GSFs), closely related to the time-frequency concentration problem on a unit disk in D. Slepian [19]. These functions form a complete orthogonal system in with , and can be viewed as a generalization of the Jacobi polynomials with parameter (α, 0). We present various analytic and asymptotic properties of GSFs, and study spectral approximations by such functions.

Keywords

33E3033C4741A3065N35Generalized Slepian functionsorthogonal systemsapproximation errorsspectral accuracy

Information

Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 4 , Issue 2 , May 2011, pp. 296 - 318
Copyright
Copyright © Global Science Press Limited 2011

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