Failure of the $L^1$ pointwise ergodic theorem for $\mathrm{PSL}_2(\mathbb{R})$
| Autor: | Peter Burton, Lewis Bowen |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Hyperbolic geometry 010102 general mathematics Algebraic geometry Dynamical Systems (math.DS) PSL 01 natural sciences Pointwise ergodic theorem Differential geometry 0103 physical sciences FOS: Mathematics 010307 mathematical physics Geometry and Topology Ball (mathematics) 0101 mathematics Mathematics - Dynamical Systems Projective geometry Mathematics |
| Popis: | Amos Nevo established the pointwise ergodic theorem in $L^p$ for measure-preserving actions of $\mathrm{PSL}_2(\mathbb{R})$ on probability spaces with respect to ball averages and every $p>1$. This paper shows by explicit example that Nevo's Theorem cannot be extended to $p=1$. 4 figures added |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|