{"ID":2844099,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.07326","arxiv_id":"2511.07326","title":"Exact output tracking for the one-dimensional heat equation and applications to the interpolation problem in Gevrey classes of order 2","abstract":"This paper provides a complete characterization of the Dirichlet boundary outputs that can be exactly tracked in the one-dimensional heat equation with Neumann boundary control. The problem consists in describing the set of boundary traces generated by square-integrable controls over a finite or infinite time horizon. We show that these outputs form a precise functional space related to Gevrey regularity of order 2. In the infinite-time case, the trackable outputs are precisely those functions whose successive derivatives satisfy a weighted summability condition, which corresponds to specific Gevrey classes. For finite-time horizons, an additional compatibility condition involving the reachable space of the system provides a full characterization. The analysis relies on Fourier-Laplace transform, properties of Hardy spaces, the flatness method, and a new Plancherel-type theorem for Hilbert spaces of Gevrey functions. Beyond control theory, our results yield an optimal solution to the classical interpolation problem in Gevrey-$2$ classes, which improves results of Mitjagin on the optimal loss factor. The techniques developed here also extend to variants of the heat system with different boundary conditions or observation points.","short_abstract":"This paper provides a complete characterization of the Dirichlet boundary outputs that can be exactly tracked in the one-dimensional heat equation with Neumann boundary control. The problem consists in describing the set of boundary traces generated by square-integrable controls over a finite or infinite time horizon....","url_abs":"https://arxiv.org/abs/2511.07326","url_pdf":"https://arxiv.org/pdf/2511.07326v2","authors":"[\"Lucas Davron\",\"Pierre Lissy\"]","published":"2025-11-10T17:28:32Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}