{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,26]],"date-time":"2026-04-26T10:00:23Z","timestamp":1777197623626,"version":"3.51.4"},"reference-count":34,"publisher":"American Mathematical Society (AMS)","issue":"270","license":[{"start":{"date-parts":[[2010,9,17]],"date-time":"2010-09-17T00:00:00Z","timestamp":1284681600000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>In this paper, the approximation properties of the prolate spheroidal wave functions of order zero (PSWFs) are studied, and a set of optimal error estimates are derived for the PSWF approximation of non-periodic functions 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 results consistent with the theoretical analysis are also presented.<\/p>","DOI":"10.1090\/s0025-5718-09-02268-6","type":"journal-article","created":{"date-parts":[[2010,2,4]],"date-time":"2010-02-04T11:19:48Z","timestamp":1265282388000},"page":"807-827","source":"Crossref","is-referenced-by-count":33,"title":["Analysis of spectral approximations using prolate spheroidal wave functions"],"prefix":"10.1090","volume":"79","author":[{"given":"Li-Lian","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2009,9,17]]},"reference":[{"key":"1","series-title":"Pure and Applied Mathematics, Vol. 65","volume-title":"Sobolev spaces","author":"Adams, Robert A.","year":"1975"},{"key":"2","isbn-type":"print","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1016\/S1570-8659(97)80003-8","article-title":"Spectral methods","author":"Bernardi, Christine","year":"1997","ISBN":"https:\/\/id.crossref.org\/isbn\/044482278X"},{"issue":"3","key":"3","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1016\/j.wavemoti.2004.05.008","article-title":"Wave propagation using bases for bandlimited functions","volume":"41","author":"Beylkin, G.","year":"2005","journal-title":"Wave Motion","ISSN":"https:\/\/id.crossref.org\/issn\/0165-2125","issn-type":"print"},{"key":"4","first-page":"931","article-title":"On the theory of spheroidal wave functions of order zero","volume":"53","author":"Bouwkamp, C. 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