On Spectral Approximations by Generalized Slepian Functions

On Spectral Approximations by Generalized Slepian Functions

Year:    2011

Numerical Mathematics: Theory, Methods and Applications, Vol. 4 (2011), Iss. 2 : pp. 296–318

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 $L^2_{\varpi_α}(-1,1)$ with $\varpi_α=(1-x)^α,$ $α>-1,$ and can be viewed as a generalization of the Jacobi polynomials with parameter $(\alpha,0)$. We present various analytic and asymptotic properties of GSFs, and study spectral approximations by such functions.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2011.42s.10

Numerical Mathematics: Theory, Methods and Applications, Vol. 4 (2011), Iss. 2 : pp. 296–318

Published online:    2011-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:    Generalized Slepian functions orthogonal systems approximation errors spectral accuracy.

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