Reachable space of the Hermite heat equation with boundary control

2021/09/01 by Andreas Hartmann, Hartmann, Andreas, Marcu-Antone Orsoni +1 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #math.AP #math.CV

paper · pdf · doi:10.48550/arxiv.2109.00243

arxiv created 2021/09/01 · openalex publication_date 2021/09/01 · arxiv updated 2021/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss reachable states for the Hermite heat equation on a segment with boundary L²-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 of the segment is the origin and when the segment is symmetric with respect to the origin. One of the main results is that reachable states extend to functions in a Bergman space on a square one diagonal of which is the segment under consideration, and that functions holomorphic in a neighborhood of this square are reachable.

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