Numer. Math. Theor. Meth. Appl., 4 (2011), pp. 296-318.
Published online: 2011-04
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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} }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.