{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,22]],"date-time":"2023-08-22T15:06:58Z","timestamp":1692716818864},"reference-count":19,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,17]],"date-time":"2023-07-17T00:00:00Z","timestamp":1689552000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Capacity building for scientific and technological innovation services\u2013basic scientific research business fees","award":["110052971921\/102"]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"In this article, we give the sharp bounds of probabilistic Kolmogorov N,\u03b4-widths and probabilistic linear N,\u03b4-widths of the multivariate Sobolev space W2A with common smoothness on a Sq norm equipped with the Gaussian measure \u03bc, where A\u2282Rd is a finite set. And we obtain the sharp bounds of average width from the results of the probabilistic widths. These results develop the theory of approximation of functions and play important roles in the research of related approximation algorithms for Sobolev spaces.<\/jats:p>","DOI":"10.3390\/axioms12070698","type":"journal-article","created":{"date-parts":[[2023,7,18]],"date-time":"2023-07-18T05:46:02Z","timestamp":1689659162000},"page":"698","source":"Crossref","is-referenced-by-count":1,"title":["N-Widths of Multivariate Sobolev Spaces with Common Smoothness in Probabilistic and Average Settings in the Sq Norm"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-5830-8417","authenticated-orcid":false,"given":"Yuqi","family":"Liu","sequence":"first","affiliation":[{"name":"College of Science, North China University of Technology, Beijing 100144, China"}]},{"given":"Xuehua","family":"Li","sequence":"additional","affiliation":[{"name":"College of Science, North China University of Technology, Beijing 100144, China"}]},{"given":"Huan","family":"Li","sequence":"additional","affiliation":[{"name":"College of Science, North China University of Technology, Beijing 100144, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,17]]},"reference":[{"key":"ref_1","first-page":"112","article-title":"Approximation of functions with bounded mixed derivative","volume":"178","author":"Temlyakov","year":"1986","journal-title":"Trudy Mat. 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(1985). n-Widths in Approximation Theory, Springer.","DOI":"10.1007\/978-3-642-69894-1"},{"key":"ref_15","first-page":"74","article-title":"Average error bounds of best approximation in a Banach space with Gaussian measure","volume":"11","author":"Sun","year":"1995","journal-title":"East J. Approx."},{"key":"ref_16","unstructured":"Guo, H.H. (1975). Lecture Notes in Mathematics, Springer."},{"key":"ref_17","unstructured":"Bogachev, V.I. (1998). Mathematics Surveys and Monographs, American Mathematical Society."},{"key":"ref_18","first-page":"916","article-title":"Kolmogorov widths of classes of periodic functions of many variables \n\t\t \n\t\t \n\t\t \n\t\t W\u02dcp\u03b1\tand H\u02dcp\u03b1 in the space Lq","volume":"49","author":"Galeev","year":"1985","journal-title":"Izv. Akad. Nauk. 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J."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/7\/698\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,19]],"date-time":"2023-07-19T06:28:09Z","timestamp":1689748089000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/7\/698"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,17]]},"references-count":19,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2023,7]]}},"alternative-id":["axioms12070698"],"URL":"http:\/\/dx.doi.org\/10.3390\/axioms12070698","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,17]]}}}
