Identifying Bergman space functions from intervals

TL;DR

This paper characterizes Bergman space functions on a square using their diagonal values and derivatives, linking this to the heat equation's controllability on an interval with boundary controls.

Contribution

It introduces a novel characterization of Bergman space functions via diagonal data, connecting complex analysis with control theory of the heat equation.

Findings

Characterization of Bergman functions through diagonal values and derivatives.

Connection established between function theory and heat equation controllability.

Provides a new perspective on boundary control problems in PDEs.

Abstract

We characterize functions of a Bergman space on a square by their values and derivatives on the diagonals. This problem is connected with the reachable space of the one-dimensional heat equation on a finite interval with boundary $L^2$-controls.