| 圆环上Dirichlet空间上的乘子 |
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| 引用本文： | 曹泽龙,刘俊麟,何莉.圆环上Dirichlet空间上的乘子[J].数学研究及应用,2018,38(2):169-182. |
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| 作者姓名： | 曹泽龙 刘俊麟 何莉 |
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| 作者单位： | 广州市执信中学, 广东 广州 510080,广州市执信中学, 广东 广州 510080,广州大学数学与信息科学学院,广东 广州 510006 |
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| 基金项目： | 国家自然科学基金(Grant No.11501136),广东省特色创新项目(Grant No.2016KTSCX105)，广州市青年项目(Grant No.1201630152). |
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| 摘 要： | 单位圆盘上的经典Dirichlet空间中的乘子比Hardy空间、Bergman空间复杂许多, 例如有界性问题是一个迄今悬而未决的问题, 很多基本问题都有待解决. 圆环作为一类典型的复连通区域, 其上的函数结构更复杂. 本文主要讨论圆环上的Dirichlet空间上乘子的可逆性与Fredholm 性质, 计算了具有洛朗多项式符号的乘子的谱与本性谱. 此外, 解决了文献6]所提出的关于一般符号乘子的谱与本性谱问题.
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| 关 键 词： | 圆环 乘子 谱 本性谱 Fredholm指标 |
| 收稿时间： | 2017/11/21 0:00:00 |
| 修稿时间： | 2018/1/13 0:00:00 |
Multipliers on the Dirichlet Space for the Annulus |
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| Zelong CAO,Junlin LIU and Li HE.Multipliers on the Dirichlet Space for the Annulus[J].Journal of Mathematical Research with Applications,2018,38(2):169-182. |
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| Authors: | Zelong CAO Junlin LIU and Li HE |
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| Institution: | Zhixin High School, Guangdong 510080, P. R. China,Zhixin High School, Guangdong 510080, P. R. China and Department of Mathematics, Guangzhou University, Guangdong 510006, P. R. China |
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| Abstract: | Multipliers on the classic Dirichlet space of the unit disk are much more complex than those on the Hardy space and the Bergman space, many basic problems have not been solved, such as the boundedness, which is still an open problem. The annulus, as a kind of typical complex connected domain, has more complicated function structure. This paper focuses on discussing the invertibility and Fredholmness of multipliers on the Dirichlet space of the annulus. The spectra and essential spectra of multipliers with Laurent polynomials symbols are calculated. In addition, we anwser a problem proposed by Guangfu CAO and Li HE on spectrum and essential spectrum for general multipliers. |
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| Keywords: | annulus multiplier spectra essential spectra |
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