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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2303.16489 |
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| _version_ | 1866914679363731456 |
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| author | Hotta, Ikkei Schleißinger, Sebastian Sugawa, Toshiyuki |
| author_facet | Hotta, Ikkei Schleißinger, Sebastian Sugawa, Toshiyuki |
| contents | In this article we prove that nonlinear resolvents of infinitesimal generators on bounded and convex subdomains of $\C^n$ are decreasing Loewner chains. Furthermore, we consider the problem of the existence of nonlinear resolvents on unbounded convex domains in $\C$. In the case of the upper half-plane, we obtain a complete solution by using that nonlinear resolvents of certain generators correspond to semigroups of probability measures with respect to free convolution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_16489 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Nonlinear resolvents and decreasing Loewner chains Hotta, Ikkei Schleißinger, Sebastian Sugawa, Toshiyuki Complex Variables Dynamical Systems Primary 37L05, Secondary 30C45, 46L54 In this article we prove that nonlinear resolvents of infinitesimal generators on bounded and convex subdomains of $\C^n$ are decreasing Loewner chains. Furthermore, we consider the problem of the existence of nonlinear resolvents on unbounded convex domains in $\C$. In the case of the upper half-plane, we obtain a complete solution by using that nonlinear resolvents of certain generators correspond to semigroups of probability measures with respect to free convolution. |
| title | Nonlinear resolvents and decreasing Loewner chains |
| topic | Complex Variables Dynamical Systems Primary 37L05, Secondary 30C45, 46L54 |
| url | https://arxiv.org/abs/2303.16489 |