{"title":"一类Gelfand-Shilov空间s - αβ的Gevrey空间表征","authors":"A.F.M. ter Elst, S.J.L. van Eijndhoven","doi":"10.1016/S1385-7258(89)80025-3","DOIUrl":null,"url":null,"abstract":"<div><p>Let <em>p,q</em> ∈ ℕ and let ϱ≥ϱ<sub><em>p,q</em></sub> with ϱ<sub><em>p,q</em></sub> = max {l/<em>p</em>, l/<em>q</em>}, ϱ<sub><em>p</em>1,</sub> = 1/<em>p</em>, and ϱ<sub>1,<em>q</em></sub>= 1/<em>q</em>, <em>p,q</em>>l. In this paper it is proved that there exist symmetric differential operators <em>A</em><sub><em>p,q</em></sub> in L<sub>2</sub>(ℝ) such that the Gelfand-Shilov space <em><strong>S</strong></em><sub><em>pϱ</em></sub><sup><em>pϱ</em></sup> is equal to the Gevrey space of order 2<em>pqϱ</em> relative to <em>A<sub>p,q</sub></em>.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"92 2","pages":"Pages 175-184"},"PeriodicalIF":0.0000,"publicationDate":"1989-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(89)80025-3","citationCount":"2","resultStr":"{\"title\":\"A Gevrey space characterization of certain Gelfand-Shilov spaces Sαβ\",\"authors\":\"A.F.M. ter Elst, S.J.L. van Eijndhoven\",\"doi\":\"10.1016/S1385-7258(89)80025-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let <em>p,q</em> ∈ ℕ and let ϱ≥ϱ<sub><em>p,q</em></sub> with ϱ<sub><em>p,q</em></sub> = max {l/<em>p</em>, l/<em>q</em>}, ϱ<sub><em>p</em>1,</sub> = 1/<em>p</em>, and ϱ<sub>1,<em>q</em></sub>= 1/<em>q</em>, <em>p,q</em>>l. In this paper it is proved that there exist symmetric differential operators <em>A</em><sub><em>p,q</em></sub> in L<sub>2</sub>(ℝ) such that the Gelfand-Shilov space <em><strong>S</strong></em><sub><em>pϱ</em></sub><sup><em>pϱ</em></sup> is equal to the Gevrey space of order 2<em>pqϱ</em> relative to <em>A<sub>p,q</sub></em>.</p></div>\",\"PeriodicalId\":100664,\"journal\":{\"name\":\"Indagationes Mathematicae (Proceedings)\",\"volume\":\"92 2\",\"pages\":\"Pages 175-184\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1989-06-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S1385-7258(89)80025-3\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indagationes Mathematicae (Proceedings)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1385725889800253\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae (Proceedings)","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1385725889800253","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Gevrey space characterization of certain Gelfand-Shilov spaces Sαβ
Let p,q ∈ ℕ and let ϱ≥ϱp,q with ϱp,q = max {l/p, l/q}, ϱp1, = 1/p, and ϱ1,q= 1/q, p,q>l. In this paper it is proved that there exist symmetric differential operators Ap,q in L2(ℝ) such that the Gelfand-Shilov space Spϱpϱ is equal to the Gevrey space of order 2pqϱ relative to Ap,q.
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