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Volume 4, Issue 2
On Spectral Approximations by Generalized Slepian Functions

Jing Zhang & Li-Lian Wang

DOI: 10.4208/nmtma.2011.42s.10

Numer. Math. Theor. Meth. Appl., 4 (2011), pp. 296-318.

Published online: 2011-04

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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 $L^2_{\varpi_α}(-1,1)$ 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.

  • Keywords

Generalized Slepian functions, orthogonal systems, approximation errors, spectral accuracy.

  • AMS Subject Headings

33E30, 33C47, 41A30, 65N35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-4-296, author = {Jing Zhang and Li-Lian Wang}, title = {On Spectral Approximations by Generalized Slepian Functions}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2011}, volume = {4}, number = {2}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2011.42s.10}, url = {http://global-sci.org/intro/article_detail/nmtma/5970.html} }
TY - JOUR T1 - On Spectral Approximations by Generalized Slepian Functions AU - Jing Zhang & Li-Lian Wang JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 296 EP - 318 PY - 2011 DA - 2011/04 SN - 4 DO - http://doi.org/10.4208/nmtma.2011.42s.10 UR - https://global-sci.org/intro/article_detail/nmtma/5970.html KW - Generalized Slepian functions, orthogonal systems, approximation errors, spectral accuracy. AB -

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.

Jing Zhang and Li-Lian Wang. (2011). On Spectral Approximations by Generalized Slepian Functions. Numerical Mathematics: Theory, Methods and Applications. 4 (2). 296-318. doi:10.4208/nmtma.2011.42s.10
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