Extension operators via semigroups

Universality and models for semigroups of operators on a Hilbert space

This paper considers universal Hilbert space operators in the sense of Rota, and gives criteria for universality of semigroups in the context of uniformly continuous semigroups and contraction semigroups. Specific examples are given. Universal semigroups provide models for these classes of semigroups: following a line of research initiated by Shimorin, models for concave semigroups are developed, in terms of shifts on reproducing kernel Hilbert spaces.

Semigroups of Composition Operators on Hardy Spaces of the half-plane

We identify the semigroups consisting of bounded composition operators on the Hardy spaces $H^p(\U)$ of the upper half-plane. We show that any such semigroup is strongly continuous on $H^p(\U)$ but not uniformly continuous and we identify the infinitesimal generator.

Semigroups of composition operators in analytic Morrey spaces

Analytic Morrey spaces belong to the class of function spaces which, like BMOA, are defined in terms of the degree of oscillation on the boundary of functions analytic in the unit disc. We consider semigroups of composition operators on these spaces and focus on the question of strong continuity. It is shown that these semigroups behave like on BMOA.

Semigroups of weighted composition operators in spaces of analytic functions

We study the strong continuity of weighted composition semigroups of the form $T_tf=φ_t'\left(f\circφ_t\right)$ in several spaces of analytic functions. First we give a general result on separable spaces and use it to prove that these semigroups are always strongly continuous in the Hardy and Bergman spaces. Then we focus on two non-separable family of spaces, the mixed norm and the weighted Banach spaces. We characterize the maximal subspace in which a semigroup of analytic functions induces a strongly continuous semigroup of weighted composition operators depending on its Denjoy-Wolff point,…

半群复合算子的无穷小生成元的特征值

Eigenvalues for Infinitesimal Generators of Semigroups of Composition Operators

研究复合算子半群的无穷小生成元在Hardy空间、Bergman空间和Dirichlet空间中的特征值，分析Holomorphic半群类型及其Koenigs域欧几里得几何对点谱特征的影响。

Semigroups of composition operators and integral operators on mixed norm spaces

We characterize the semigroups of composition operators that are strongly continuous on the mixed norm spaces $H(p,q,α)$. First, we study the separable spaces $H(p,q,α)$ with $q<\infty,$ that behave as the Hardy and Bergman spaces. In the second part we deal with the spaces $H(p,\infty,α),$ where polynomials are not dense. To undertake this study, we introduce the integral operators, characterize its boundedness and compactness, and use its properties to find the maximal closed linear subspace of $H(p,\infty,α)$ in which the semigroups are strongly continuous. In particular, we obtain that thi…