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 |
圆环上Dirichlet空间上的乘子 |
Multipliers on the Dirichlet Space for the Annulus |
投稿时间:2017-11-21 修订日期:2018-01-13 |
DOI:10.3770/j.issn:2095-2651.2018.02.007 |
中文关键词: 圆环 乘子 谱 本性谱 Fredholm指标 |
英文关键词:annulus multiplier spectra essential spectra |
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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中文摘要: |
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. |
英文摘要: |
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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