Dirichlet-to-Robin Operators via Composition Semigroups

TL;DR

This paper establishes well-posedness for an evolution problem involving Dirichlet-to-Robin operators and reveals a connection between the generated semigroup and weighted composition operators on analytic function spaces.

Contribution

It introduces a novel analysis of Dirichlet-to-Robin operators, linking their semigroup generation to weighted composition operators on Banach spaces of analytic functions.

Findings

Proves well-posedness of the evolution problem.

Identifies the semigroup as a weighted composition operator.

Establishes a connection between boundary operators and analytic function spaces.

Abstract

We show well-posedness for an evolution problem associated with the Dirichlet-to-Robin operator for certain Robin boundary data. Moreover, it turns out that the semigroup generated by the Dirichlet-to-Robin operator is closely related to a weighted semigroup of composition operators on an appropriate Banach space of analytic functions.