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 - <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>