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arXiv · 2303.16489

Nonlinear resolvents and decreasing Loewner chains

Ikkei Hotta·Sebastian Schleißinger·Toshiyuki Sugawa
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Abstract

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.

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Ikkei Hotta, Sebastian Schleißinger, Toshiyuki Sugawa. 2023-03-29. Nonlinear resolvents and decreasing Loewner chains. https://arxiv.org/abs/2303.16489

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