Pluripotential theory, semigroups and boundary behavior of infinitesimal generators in strongly convex domains

由加倍权诱导的加权Bergman空间上复合半群的无穷小生成元的谱

Spectra of infinitesimal generators of composition semigroups on weighted Bergman spaces induced by doubling weights

本文研究椭圆型复合半群在加倍权加权Bergman空间上诱导的复合半群的无穷小生成元的谱，利用谱映射定理和复合算子谱刻画，并探讨最终范数连续性及紧积分算子。

Regular poles and $β$-numbers in the theory of holomorphic semigroups

We introduce the notion of regular (boundary) poles for infinitesimal generators of semigroups of holomorphic self-maps of the unit disc. We characterize such regular poles in terms of $β$-points (i.e. pre-images of values with positive Carleson-Makarov $β$-numbers) of the associated semigroup and of the associated Königs intertwining function. We also define a natural duality operation in the cone of infinitesimal generators and show that the regular poles of an infinitesimal generator correspond to the regular null poles of the dual generator. Finally we apply such a construction to study ra…

无穷小生成元的滤过（参数嵌入）研究综述

Survey on filtrations (parametric embeddings) of infinitesimal generators

本文针对单位圆盘内半群生成元的滤过理论，总结已有滤过的共性与特性，研究新型滤过与几何函数论的关联及半群动力学性质，并在多类滤过与非线性预解式上求解Fekete–Szegö问题。

A Rigidity Condition for Holomorphic Generator in Strongly Convex Domains

In this paper I give a condition, in terms of boundary behaviour, that forces the infinitesimal generator of a one-parameter semigroup of holomorphic maps to vanish.

Weighted composition semigroups on Banach spaces of holomorphic functions

We study, to certain Banach spaces $X$, families of weighted composition operators. Notably, we show that if this family form a strongly continuous semigroup, then its infinitesimal generator ($Γ, D(Γ)$) is given by $Γf = gf+Gf^\prime$ with $D(Γ) = \{ f\in X \ | \ gf+Gf^\prime\in X \}$ where $g, G$ are holomorphic functions. Moreover, our second maim result is to study the reciprocal implication. That is if $(Γ, D(Γ))$, define like above, generate a strongly continuous semigroup, then this one is a family of weighted composition operators.

Aleksandrov-Clark measures and semigroups of analytic functions in the unit disc

In this paper we prove a formula describing the infinitesimal generator of a continuous semigroup $(\v_t)$ of holomorphic self-maps of the unit disc with respect to a boundary regular fixed point. The result is based on Alexandrov-Clark measures techniques. In particular we prove that the Alexandrov-Clark measure of $(\v_t)$ at a boundary regular fixed points is differentiable (in the weak$^\ast$-topology) with respect to $t$.

精确系数与反问题对于全纯半群生成元

Sharp Coefficient and Inverse Problems for Holomorphic Semigroup Generators

本文研究了与全纯半群生成元相关系数函数的极值问题，得出了关于初始对数系数、反系数及对数反系数的精确界，并探讨了连续系数问题及广义Fekete--Szegö函数的极值。

非线性预解式与递减 Loewner 链

Nonlinear resolvents and decreasing Loewner chains

本文证明了 $\C^n$ 有界凸子域上无穷小生成元的非线性预解式构成递减 Loewner 链，并利用自由卷积下半群性质解决了上半平面无界凸域上预解式的存在性问题。

Geometric properties of the nonlinear resolvent of holomorphic generators

Let $f$ be the infinitesimal generator of a one-parameter semigroup $\left\{ F_{t}\right\} _{t\ge0}$ of holomorphic self-mappings of the open unit disk $Δ$. In this paper we study properties of the family $R$ of resolvents $(I+rf)^{-1}:Δ\toΔ~ (r\ge0)$ in the spirit of geometric function theory. We discovered, in particular, that $R$ forms an inverse Löwner chain of hyperbolically convex functions. Moreover, each element of $R$ satisfies the Noshiro-Warschawski condition and is a starlike function of order at least $\frac12$,. This, in turn, implies that each element of $R$ is also a holomorphi…

关于抛物型Koenigs域的频率

On frequencies of parabolic Koenigs domains

本文研究单位圆盘上抛物型解析半群对应的Hardy空间复合算子半群无穷小生成元的点谱，将其归约为Koenigs域的频率刻画问题，利用域的几何性质与边界调和测度估计推导点谱包含关系与充分刻画条件，推广了双曲半群的相关结果。