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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.06076 |
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| _version_ | 1866908870146785280 |
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| author | Maslyuchenko, Oleksandr V. Morawiec, Janusz Zürcher, Thomas |
| author_facet | Maslyuchenko, Oleksandr V. Morawiec, Janusz Zürcher, Thomas |
| contents | We investigate a linear operator associated with a functional equation that arises from studying some class of invariant measures under multidimensional transformations. By examining its iterates, we derive an explicit solution formula for the functional equation in some class of functions and establish a result on the existence of an absolutely continuous invariant measure under a multidimensional transformation that can be viewed as a generalization of classical $p$-adic maps to higher dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06076 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Operators arising from invariant measures under some class of multidimensional transformations Maslyuchenko, Oleksandr V. Morawiec, Janusz Zürcher, Thomas Functional Analysis Primary 47A50, Secondary 47A60, 39B12, 26A16 We investigate a linear operator associated with a functional equation that arises from studying some class of invariant measures under multidimensional transformations. By examining its iterates, we derive an explicit solution formula for the functional equation in some class of functions and establish a result on the existence of an absolutely continuous invariant measure under a multidimensional transformation that can be viewed as a generalization of classical $p$-adic maps to higher dimensions. |
| title | Operators arising from invariant measures under some class of multidimensional transformations |
| topic | Functional Analysis Primary 47A50, Secondary 47A60, 39B12, 26A16 |
| url | https://arxiv.org/abs/2603.06076 |