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In this paper, we solve a separation of singularities problem in the Bergman space. More precisely, we show that if $Psubset mathbb{C}$ 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].
We analyze Bergman spaces A p f (D) of generalized analytic functions of solutions to the Vekua equation $partial$w = ($partial$f /f)w in the unit disc of the complex plane, for Lipschitz-smooth non-vanishing real valued functions f and 1 < p < $inft
We discuss reachable states for the Hermite heat equation on a segment with boundary $L^2$-controls. The Hermite heat equation corresponds to the heat equation to which a quadratic potential is added. We will discuss two situations: when one endpoint
The objective of this paper is twofold. First we provide the -- to the best knowledge of the authors -- first result on the behavior of the regular part of the free boundary of the obstacle problem close to singularities. We do this using our second
If $U:[0,+infty[times M$ is a uniformly continuous viscosity solution of the evolution Hamilton-Jacobi equation $$partial_tU+ H(x,partial_xU)=0,$$ where $M$ is a not necessarily compact manifold, and $H$ is a Tonelli Hamiltonian, we prove the set $Si
Following upon results of Putinar, Sun, Wang, Zheng and the first author, we provide models for the restrictions of the multiplication by a finite Balschke product on the Bergman space in the unit disc to its reducing subspaces. The models involve a