Infinitesimal generators of semigroups with prescribed boundary fixed points

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。

On the Königs function of semigroups of holomorphic self-maps of the unit disc

Let $(ϕ_t)$ be a semigroup of holomorphic self-maps of~$\mathbb D$. In this note, we use an abstract approach to define the Königs function of $(ϕ_t)$ and "holomorphic models" and show how to deduce the existence and properties of the infinitesimal generator of $(ϕ_t)$ from this construction.

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.

连续动力学中的极值收敛速率

Extremal rate of convergence in continuous dynamics

本文刻画上半平面全纯自映射半群以最慢速率收敛至Denjoy--Wolff点的条件，重点解决抛物情形，并利用Herglotz表示与Koenigs函数共形性提供多种等价描述。

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 $t$.

A class of quasicontractive semigroups acting on Hardy and Dirichlet space

This paper provides a complete characterization of quasicontractive $C_0$-semigroups on Hardy and Dirichlet space with a prescribed generator of the form $Af=Gf'$. We show that such semigroups are semigroups of composition operators and we give simple sufficient and necessary condition on $G$. Our techniques are based on ideas from semigroup theory, such as the use of numerical ranges.

关于连续半群的一致收敛性

On the uniform convergence of continuous semigroups

本文研究复平面区域上连续半群的一致收敛性，将单位圆盘上 Gumenyuk 的结果加强为最优速率 O(√t)，并利用无穷小生成元刻画右半平面上半群一致收敛到恒等映射的条件。

On nonnegatively graded Weierstrass points

We provide a new lower bound for the dimension of the moduli space of smooth pointed curves with prescribed Weierstrass semigroup at the marked point, derived from the Deligne-Greuel formula and Pinkham's equivariant deformation theory. Using Buchweitz's description of the first cohomology module of the cotangent complex for monomial curves, we show that our lower bound improves a recently one given by Pflueger. By allowing semigroups running over suitable families of symmetric semigroups of multiplicity six, we show that this new lower bound is attained, and that the corresponding moduli spac…

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。

Loewner Theory for Bernstein functions I: evolution families and differential equations

One-parameter semigroups of holomorphic functions appear naturally in various applications of Complex Analysis, and in particular, in the theory of (temporally) homogeneous Markov processes. A suitable analogue of one-parameter semigroups in the inhomogeneous setting is the notion of a (reverse) evolution family. In this paper we study evolution families formed by Bernstein functions, which play the role of Laplace exponents for inhomogeneous continuous-state branching processes. In particular, we characterize all Herglotz vector fields that generate such evolution families and give a complex-…