Abstract
We use some results from the theory of reproducing kernel Hilbert spaces to show that the reachable space of the heat equation for a finite rod with either one or two Dirichlet boundary controls is a RKHS of analytic functions on a square, and we compute its reproducing kernel as an infinite double series. We also show that the null reachable space of the heat equation for the half line with Dirichlet boundary data is a RKHS of analytic functions on a sector, whose reproducing kernel is (essentially) the sum of pullbacks of the Bergman and Hardy kernels on the half plane \(\mathbb {C}^+\).
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The author thanks the referee for the suggestions he/she made to improve this work.
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The author was partially supported by Project PAPIIT IN100919 of DGAPA-UNAM, and Project A1-S-17475 of Conacyt-México.
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López-García, M. The Reachable Space of the Heat Equation for a Finite Rod as a Reproducing Kernel Hilbert Space. Integr. Equ. Oper. Theory 93, 46 (2021). https://doi.org/10.1007/s00020-021-02660-6
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DOI: https://doi.org/10.1007/s00020-021-02660-6