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

We use some results from the theory of reproducing kernel Hilbert spaces to show that reachable space heat equation for a finite rod with either one or two Dirichlet boundary controls is RKHS analytic functions on square, and we compute its as an infinite double series. also null half line data sector, whose (essentially) sum pullbacks Bergman Hardy kernels plane \(\mathbb {C}^+\).