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The Reachable Space of the Heat Equation for a Finite Rod as a Reproducing Kernel Hilbert Space

Authors
  • López-García, Marcos1
  • 1 Universidad Nacional Autónoma de México, Cuernavaca, MOR, 62251, Mexico , Cuernavaca (Mexico)
Type
Published Article
Journal
Integral Equations and Operator Theory
Publisher
Springer International Publishing
Publication Date
Jul 10, 2021
Volume
93
Issue
4
Identifiers
DOI: 10.1007/s00020-021-02660-6
Source
Springer Nature
Keywords
Disciplines
  • Article
License
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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 C+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {C}^+$$\end{document}.

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