{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T00:35:15Z","timestamp":1759970115297,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,1,6]],"date-time":"2025-01-06T00:00:00Z","timestamp":1736121600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["52472368"],"award-info":[{"award-number":["52472368"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This article primarily examines the approximation properties of a weighted Sobolev space W2,\u03bar defined on a sphere Sd\u22121 equipped with Gaussian measures. Specifically, this study focuses on both the average case and probabilistic case settings. The exact asymptotic orders of the Gel\u2019fand n-width and the linear n-width of W2,\u03bar on Sd\u22121 are derived for these settings, providing a comprehensive understanding of their approximation characteristics.<\/jats:p>","DOI":"10.3390\/axioms14010042","type":"journal-article","created":{"date-parts":[[2025,1,6]],"date-time":"2025-01-06T10:40:52Z","timestamp":1736160052000},"page":"42","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Approximation Characteristics of Weighted Sobolev Spaces on Sphere in Different Settings"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-0941-0665","authenticated-orcid":false,"given":"Jiayi","family":"Qiu","sequence":"first","affiliation":[{"name":"School of Science, Xihua University, Chengdu 610039, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3742-2541","authenticated-orcid":false,"given":"Guanggui","family":"Chen","sequence":"additional","affiliation":[{"name":"Yibin Campus, Xihua University, Yibin 644005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3885-770X","authenticated-orcid":false,"given":"Yanyan","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Science, Xihua University, Chengdu 610039, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ying","family":"Luo","sequence":"additional","affiliation":[{"name":"School of Science, Xihua University, Chengdu 610039, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hang","family":"Ren","sequence":"additional","affiliation":[{"name":"School of Science, Xihua University, Chengdu 610039, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,6]]},"reference":[{"key":"ref_1","unstructured":"Traub, J., Wasilkowski, G.W., and Wo\u017aniakowski, H. 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