TY - JOUR T1 - On Spectral Approximations by Generalized Slepian Functions 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.