Distributions and Analytic Continuation of Dirichlet Series

Bernoulli Operators and Dirichlet Series

We introduce and study some (infinite order) discrete derivative operators called Bernoulli operators. They are associated to a class of power series (tame power series), which include power series that converge in the unit disk, have at most a pole singularity at $z=1$, and have analytic continuation to the unit disk centered at $z=1$ with possible isolated singularities of Mittag-Leffler type. We show that they all naturally act on, and take values into, the vector space of functions $f(s,t)$ in the image of the Laplace-Mellin transform that have (single valued) analytic continuation to the …

Dirichlet级数的Hardy空间中的均值、阶与收敛性

Mean values, order, and convergence in the Hardy space of Dirichlet series

本文研究Dirichlet级数Hardy空间中范数均值公式的适用条件，放宽解析延拓有界性假设，在解析延拓的阶和收敛横坐标两个方向获得最优结果，并推广Landau--Schnee定理及解决McCarthy问题。

Composition Operators on Dirichlet Spaces over the Half-plane

As continuation of the study of polynomial approximation and composition operators on Dirichlet spaces of unit disk, which has settled a problem posed by Cima in 1976, the present paper aims to consider the case of the unbounded domains, such as the half-plane. Specifically, we may obtain the rational approximations in the Dirichlet spaces and characterize the composition operators which has dense range on the Dirichlet spaces over the half-plane. Moreover, this paper also considers the relationship between the Dirichlet spaces and Hardy spaces on half-plane.

加权 $H$-调和 Bergman 空间的解析延拓

Analytic continuation of weighted $H$-harmonic Bergman spaces

本文部分解决了 Blaschke 等人提出的关于加权 $H$-调和 Bergman 空间解析延拓的问题，识别了离散 Wallach 集并揭示了结构依赖于维数奇偶性。

Cowen-Douglas 算子与解析延拓

Cowen-Douglas operators and analytic continuation

本文研究了解析函数 Banach 空间上左可逆乘法算子的左逆作为 Cowen-Douglas 算子的条件，并探讨了该算子不变子空间中函数的解析延拓与其限制谱之间的关系。