Ergodic Properties of Composition Semigroups on the Disc Algebra
| Autor: | Leonhard Frerick, Alberto Rodríguez-Arenas, Jochen Wengenroth |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Mathematics::Functional Analysis
Mathematics::Complex Variables Semigroup Applied Mathematics 010102 general mathematics Ergodicity Holomorphic function Composition (combinatorics) Operator theory Space (mathematics) 01 natural sciences Algebra Computational Mathematics Computational Theory and Mathematics 0103 physical sciences Domain (ring theory) Ergodic theory 010307 mathematical physics 0101 mathematics Mathematics |
| Zdroj: | Complex Analysis and Operator Theory. 15 |
| ISSN: | 1661-8262 1661-8254 |
| DOI: | 10.1007/s11785-021-01105-7 |
| Popis: | Every semigroup $$\{\varphi _t\}_{t\ge 0}$$ of self-maps of the disc defines a semigroup $$\{C_{\varphi _t}\}_{t\ge 0}$$ of compositions operators on the space of holomorphic functions on the disc. We characterize the (uniform) mean ergodicity (in the sense of continuous means) and the asymptotic behaviour of these operators when they define a $$C_0$$ -semigroup on the disc algebra, in terms of the Denjoy–Wolff point and the associated planar domain in the sense of Berkson and Porta. Finally we deal with the case of Hardy and Bergman spaces. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink