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| Format: | Preprint |
| Published: |
2018
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| Online Access: | https://arxiv.org/abs/1806.06197 |
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| _version_ | 1866910126321958912 |
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| author | Okamura, Kazuki |
| author_facet | Okamura, Kazuki |
| contents | In this paper we consider a class of conjugate equations, which generalizes de Rham's functional equations. We give sufficient conditions for existence and uniqueness of solutions under two different series of assumptions. We consider regularity of solutions. In our framework, two iterated function systems are associated with a series of conjugate equations. We state local regularity by using the invariant measures of the two iterated function systems with a common probability vector. We give several examples, especially an example such that infinitely many solutions exists, and a new class of fractal functions on the two-dimensional standard Sierpinski gasket which are not harmonic functions or fractal interpolation functions. We also consider a certain kind of stability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1806_06197 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Some results for conjugate equations Okamura, Kazuki Classical Analysis and ODEs Dynamical Systems 39B72, 39B12, 28A80, 26A30 In this paper we consider a class of conjugate equations, which generalizes de Rham's functional equations. We give sufficient conditions for existence and uniqueness of solutions under two different series of assumptions. We consider regularity of solutions. In our framework, two iterated function systems are associated with a series of conjugate equations. We state local regularity by using the invariant measures of the two iterated function systems with a common probability vector. We give several examples, especially an example such that infinitely many solutions exists, and a new class of fractal functions on the two-dimensional standard Sierpinski gasket which are not harmonic functions or fractal interpolation functions. We also consider a certain kind of stability. |
| title | Some results for conjugate equations |
| topic | Classical Analysis and ODEs Dynamical Systems 39B72, 39B12, 28A80, 26A30 |
| url | https://arxiv.org/abs/1806.06197 |