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arXiv · 2104.05268

Separation of singularities for the Bergman space and application to control theory

Andreas Hartmann·Marcu-Antone Orsoni
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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 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].

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Andreas Hartmann, Marcu-Antone Orsoni. 2021-04-12. Separation of singularities for the Bergman space and application to control theory. https://doi.org/10.1016/j.matpur.2021.04.009

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