The reachable space of the heat equation for a finite rod as a\n Reproducing Kernel Hilbert Space

2019/10/08 by Marcos López-García, Lopez-Garcia, Marcos
Mathematics · #35K05 #46E22 #93B03 #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #FOS: Mathematics #Holomorphic and Operator Theory #Optimization and Control (math.OC) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1910.03765

openalex publication_date 2019/10/08 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

We use some results from the theory of Reproducing Kernel Hilbert Spaces to\nshow that the reachable space of the heat equation for a finite rod with either\none or two Dirichlet boundary controls is a RKHS of analytic functions on a\nsquare, and we compute its reproducing kernel. We also show that the null\nreachable space of the heat equation for the half line with Dirichlet boundary\ndata is a RKHS of analytic functions on a sector, whose reproducing kernel is\n(essentially) the sum of pullbacks of the Bergman and Hardy kernels on the half\nplane \ℂ⁺. We also consider the case with Neumann boundary data.\n

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