Separation of singularities for the Bergman space and application to control theory
Language
en
Article de revue
This item was published in
Journal de Mathématiques Pures et Appliquées. 2021, vol. 150, p. 181-201
Elsevier
English Abstract
In this paper, we solve a separation of singularities problem in the Bergman space. More precisely, we show that if $P\subset \mathbb{C}$ is a convex polygon which is the intersection of $n$ half planes, then the Bergman ...Read more >
In this paper, we solve a separation of singularities problem in the Bergman space. More precisely, we show that if $P\subset \mathbb{C}$ is a convex polygon which is the intersection of $n$ half planes, then the Bergman space on $P$ decomposes into the sum of the Bergman spaces on these half planes. The result applies to the characterization of the reachable space of the one-dimensional heat equation on a finite interval with boundary controls. We prove that this space is a Bergman space of the square which has the given interval as a diagonal. This gives an affirmative answer to a conjecture raised in [HKT20].Read less <
ANR Project
Méthodes variationnelles pour les signaux sur graphe - ANR-18-CE40-0005
Origin
Hal imported