Identifying Bergman space functions from intervals

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.

New version: we improved the main result (Theorem 4.1) replacing the equivalence between the two expressions by an equality. We also corrected some typos. 22 pages, 5 figures