作用于解析函数的某些希尔伯特空间的复合微分算子

IF 0.7 4区数学 Q2 MATHEMATICS

Hacettepe Journal of Mathematics and Statistics Pub Date : 2023-06-13 DOI:10.15672/hujms.1241783

Yazdan Bayat, A. Abkar

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引用次数: 0

摘要

研究了作用于单位圆盘的Bergman和Dirichlet空间上的复合微分算子。我们首先刻画了这个算子在加权Bergman空间上的紧性。然后我们将证明对于单位磁盘$\磁盘$上的解析自映射$\varphi$，当且仅当$\varphi$是一元且多项式在$\varphi(\disk)$上的Bergman空间上是稠密的，诱导复合微分算子是有界的。

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Composition-differentiation operators acting on certain Hilbert spaces of analytic functions

We study composition-differentiation operators acting on the Bergman and Dirichlet space of the unit disk. We first characterize the compactness of this operator on weighted Bergman spaces. We shall then prove that for an analytic self-map $\varphi$ on the unit disk $\disk$, the induced composition-differentiation operator is bounded with dense range if and only if $\varphi$ is univalent and the polynomials are dense in the Bergman space on $\varphi(\disk)$.

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来源期刊

Hacettepe Journal of Mathematics and Statistics 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

100

审稿时长

6-12 weeks

期刊介绍： Hacettepe Journal of Mathematics and Statistics covers all aspects of Mathematics and Statistics. Papers on the interface between Mathematics and Statistics are particularly welcome, including applications to Physics, Actuarial Sciences, Finance and Economics. We strongly encourage submissions for Statistics Section including current and important real world examples across a wide range of disciplines. Papers have innovations of statistical methodology are highly welcome. Purely theoretical papers may be considered only if they include popular real world applications.