Analysis of spectral approximations using prolate spheroidal wave functions

Abstract

In this paper, the approximation properties of the prolate spher- oidal wave functions of order zero (PSWFs) are studied, and a set of optimal error estimates are derived for the PSWF approximation of non-periodic func- tions in Sobolev spaces. These results serve as an indispensable tool for the analysis of PSWF spectral methods. A PSWF spectral-Galerkin method is proposed and analyzed for elliptic-type equations. Illustrative numerical re- sults consistent with the theoretical analysis are also presented.