Nonlinear resolvents and decreasing Loewner chains

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.

This version of the article has been accepted for publication, and is subject to Springer Nature's AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/ 10.1007/s12220-023-01544-y