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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