{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T13:34:18Z","timestamp":1775828058171,"version":"3.50.1"},"reference-count":38,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2009,11]]},"abstract":"<jats:p> The main purpose of this paper is to survey some of the work on spherical approximation done by the BNU group under the direction of Professor Sun. <\/jats:p><jats:p> The equiconvergent operators of Ces\u00e0ro means, and their interesting applications are described. The Jackson inequality for spherical polynomials and some moduli of smoothness on the sphere are investigated. The equivalence between moduli of smoothness and K-functionals is also discussed. We also describe several weighted polynomial inequalities on the sphere, including the Remez-type and the Nikolskii-type inequalities, the Marcinkiewicz\u2013Zygmund inequality, the Bernstein-type and the Schur-type inequalities. Positive cubature formulas on the sphere, and their relation to the Marcinkiewicz\u2013Zygmund inequality are also discussed. A survey on recent results on asymptotic orders of the n-widths of Sobolev's classes on the sphere is also given. <\/jats:p>","DOI":"10.1142\/s0219691309003239","type":"journal-article","created":{"date-parts":[[2009,12,8]],"date-time":"2009-12-08T04:36:16Z","timestamp":1260246976000},"page":"749-771","source":"Crossref","is-referenced-by-count":3,"title":["A SURVEY OF POLYNOMIAL APPROXIMATION ON THE SPHERE"],"prefix":"10.1142","volume":"07","author":[{"given":"FENG","family":"DAI","sequence":"first","affiliation":[{"name":"Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"KUNYANG","family":"WANG","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, P. R. 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