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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.11065 |
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Table of Contents:
- We provide a complex-analytic approach to the classification of stationary probability measures on $S^1$ with respect to the action of $PSU(1,1)$ on the unit circle via Möbius transformations by studying their Cauchy transforms from the perspective of generalized analytic continuation. We improve upon results of Bourgain and present a complete characterization of Furstenberg measures for Fuchsian groups of first kind via the Brown-Shields-Zeller theorem.