Mehmet Çelik, Luke Duane-Tessier, Ashley Marcial Rodriguez, Daniel Rodriguez, Aden Shaw
{"title":"解析图和算子下的面积差异","authors":"Mehmet Çelik, Luke Duane-Tessier, Ashley Marcial Rodriguez, Daniel Rodriguez, Aden Shaw","doi":"10.21136/cmj.2024.0023-24","DOIUrl":null,"url":null,"abstract":"<p>Motivated by the relationship between the area of the image of the unit disk under a holomorphic mapping <i>h</i> and that of <i>zh</i>, we study various <i>L</i><sup>2</sup> norms for <i>T</i><sub><i>ϕ</i></sub>(<i>h</i>), where <i>T</i><sub><i>ϕ</i></sub> is the Toeplitz operator with symbol <i>ϕ</i>. In Theorem 2.1, given polynomials <i>p</i> and <i>q</i> we find a symbol <i>ϕ</i> such that <i>T</i><sub><i>ϕ</i></sub>(<i>p</i>) = <i>q</i>. We extend some of our results to the polydisc.</p>","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"13 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Area differences under analytic maps and operators\",\"authors\":\"Mehmet Çelik, Luke Duane-Tessier, Ashley Marcial Rodriguez, Daniel Rodriguez, Aden Shaw\",\"doi\":\"10.21136/cmj.2024.0023-24\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Motivated by the relationship between the area of the image of the unit disk under a holomorphic mapping <i>h</i> and that of <i>zh</i>, we study various <i>L</i><sup>2</sup> norms for <i>T</i><sub><i>ϕ</i></sub>(<i>h</i>), where <i>T</i><sub><i>ϕ</i></sub> is the Toeplitz operator with symbol <i>ϕ</i>. In Theorem 2.1, given polynomials <i>p</i> and <i>q</i> we find a symbol <i>ϕ</i> such that <i>T</i><sub><i>ϕ</i></sub>(<i>p</i>) = <i>q</i>. We extend some of our results to the polydisc.</p>\",\"PeriodicalId\":50596,\"journal\":{\"name\":\"Czechoslovak Mathematical Journal\",\"volume\":\"13 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2024-06-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Czechoslovak Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.21136/cmj.2024.0023-24\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Czechoslovak Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.21136/cmj.2024.0023-24","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Area differences under analytic maps and operators
Motivated by the relationship between the area of the image of the unit disk under a holomorphic mapping h and that of zh, we study various L2 norms for Tϕ(h), where Tϕ is the Toeplitz operator with symbol ϕ. In Theorem 2.1, given polynomials p and q we find a symbol ϕ such that Tϕ(p) = q. We extend some of our results to the polydisc.
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