Boundary white noise in the 1D heat equation yields holomorphic extensions to a rhombus and continuous versions in weighted Bergman spaces, with the result shown to be optimal.
Weiss,Admissible observation operators for linear semigroups, Israel Journal of Mathematics 65(1989), no
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Bergman-space regularity for the heat equation with white-noise boundary forcing
Boundary white noise in the 1D heat equation yields holomorphic extensions to a rhombus and continuous versions in weighted Bergman spaces, with the result shown to be optimal.