{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T03:53:48Z","timestamp":1761710028537,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,8,22]],"date-time":"2023-08-22T00:00:00Z","timestamp":1692662400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Foundation of Dean of College of Science","award":["110051360022XN128","110051360002"],"award-info":[{"award-number":["110051360022XN128","110051360002"]}]},{"name":"Initial Research Fund of North China University of Technology","award":["110051360022XN128","110051360002"],"award-info":[{"award-number":["110051360022XN128","110051360002"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we study the probabilistic Gel\u2019fand\u00a0N,\u03b4-width of multivariate Sobolev spaces\u00a0MW2rTd\u00a0with mixed derivative that are equipped with Gaussian measure\u00a0\u03bc\u00a0in\u00a0LqTd. The sharp asymptotic estimates are determined by employing the discretization method.<\/jats:p>","DOI":"10.3390\/axioms12090804","type":"journal-article","created":{"date-parts":[[2023,8,22]],"date-time":"2023-08-22T09:10:56Z","timestamp":1692695456000},"page":"804","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Approximation Characteristics of Gel\u2019fand Type in Multivariate Sobolev Spaces with Mixed Derivative Equipped with Gaussian Measure"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/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"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huan","family":"Li","sequence":"additional","affiliation":[{"name":"College of Science, North China University of Technology, Beijing 100144, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuehua","family":"Li","sequence":"additional","affiliation":[{"name":"College of Science, North China University of Technology, Beijing 100144, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Pinkus, A. 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