Abstract
We study the Korenblum Maximum Principle for various weighted Fock spaces. The main tool relies on applying special cases of Ramanujan's Master Theorem involving the Gamma function and the Mellin transform of the Dirichlet series. It is interesting that with elementary probe functions, we still can obtain closed-form upper bound expressions, in terms of several well-known special functions, for the Korenblum constants of various weighted Fock spaces. For the first time, we obtain upper bounds of the Korenblum constant for the finite and infinite intersections of weighted Fock spaces and proved that the Korenblum Maximum Principle fails for those infinite intersections of weighted Fock spaces. Some open questions are provided.
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