复倍Fock Hilbert空间上Toeplitz算子的Fredholm理论

Pub Date : 2020-09-03 DOI:10.7146/MATH.SCAND.A-120920

Aamena Al-Qabani, T. Hilberdink, J. Virtanen

{"title":"复倍Fock Hilbert空间上Toeplitz算子的Fredholm理论","authors":"Aamena Al-Qabani, T. Hilberdink, J. Virtanen","doi":"10.7146/MATH.SCAND.A-120920","DOIUrl":null,"url":null,"abstract":"We study the Fredholm properties of Toeplitz operators acting on doubling Fock Hilbert spaces, and describe their essential spectra for bounded symbols of vanishing oscillation. We also compute the index of these Toeplitz operators in the special case when $\\varphi (z) = \\lvert {z}\\rvert^{\\beta }$ with $\\beta >0$. Our work extends the recent results on Toeplitz operators on the standard weighted Fock spaces to the setting of doubling Fock spaces.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Fredholm theory of Toeplitz operators on doubling Fock Hilbert spaces\",\"authors\":\"Aamena Al-Qabani, T. Hilberdink, J. Virtanen\",\"doi\":\"10.7146/MATH.SCAND.A-120920\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the Fredholm properties of Toeplitz operators acting on doubling Fock Hilbert spaces, and describe their essential spectra for bounded symbols of vanishing oscillation. We also compute the index of these Toeplitz operators in the special case when $\\\\varphi (z) = \\\\lvert {z}\\\\rvert^{\\\\beta }$ with $\\\\beta >0$. Our work extends the recent results on Toeplitz operators on the standard weighted Fock spaces to the setting of doubling Fock spaces.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2020-09-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.7146/MATH.SCAND.A-120920\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7146/MATH.SCAND.A-120920","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 3

摘要

我们研究了Toeplitz算子在二重Fock-Hilbert空间上的Fredholm性质，并描述了它们对于消失振荡的有界符号的本质谱。在$\varphi（z）=\lvert｛z｝\rvert ^｛\beta｝$且$\beta＞0$的特殊情况下，我们还计算了这些Toeplitz算子的索引。我们的工作将最近关于标准加权Fock空间上Toeplitz算子的结果推广到加倍Fock空间的设置。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

Fredholm theory of Toeplitz operators on doubling Fock Hilbert spaces

We study the Fredholm properties of Toeplitz operators acting on doubling Fock Hilbert spaces, and describe their essential spectra for bounded symbols of vanishing oscillation. We also compute the index of these Toeplitz operators in the special case when $\varphi (z) = \lvert {z}\rvert^{\beta }$ with $\beta >0$. Our work extends the recent results on Toeplitz operators on the standard weighted Fock spaces to the setting of doubling Fock spaces.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助