Van der Corput's difference theorem for amenable groups and the left regular representation
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916449906327552 |
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| author | Farhangi, Sohail |
| author_facet | Farhangi, Sohail |
| contents | We establish a connection between two variants of van der Corput's Difference Theorem (vdCDT) for countably infinite amenable groups $G$ and the ergodic hierarchy of mixing properties of a unitary representation $U$ of $G$. In particular, we show that one variant of vdCDT corresponds to subrepresentations of the left regular representation, and another variant of vdCDT corresponds to the absence of finite dimensional subrepresentations. We then obtain applications for measure preserving actions of countably infinite abelian groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_05560 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Van der Corput's difference theorem for amenable groups and the left regular representation Farhangi, Sohail Dynamical Systems Representation Theory Spectral Theory 22D40, 37A30, 22D10, 37A46, 37A25 We establish a connection between two variants of van der Corput's Difference Theorem (vdCDT) for countably infinite amenable groups $G$ and the ergodic hierarchy of mixing properties of a unitary representation $U$ of $G$. In particular, we show that one variant of vdCDT corresponds to subrepresentations of the left regular representation, and another variant of vdCDT corresponds to the absence of finite dimensional subrepresentations. We then obtain applications for measure preserving actions of countably infinite abelian groups. |
| title | Van der Corput's difference theorem for amenable groups and the left regular representation |
| topic | Dynamical Systems Representation Theory Spectral Theory 22D40, 37A30, 22D10, 37A46, 37A25 |
| url | https://arxiv.org/abs/2308.05560 |