@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 = {<p style="text-align: justify;">We introduce a family of orthogonal functions, termed as generalized Slepian
functions (GSFs), &nbsp;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 $\varpi_α=(1-x)^α,$
$α&gt;-1,$ 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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2011.42s.10},
url = {http://global-sci.org/intro/article_detail/nmtma/5970.html}
}