On the converse of the Shimorin--Pel\'aez--R\"atty\"a--Wick theorem
Abstract
We establish a converse of the Shimorin--Pel\'aez--R\"atty\"a--Wick theorem. Specifically, we obtain necessary and sufficient conditions for a Shimorin kernel to be the kernel of a radial, logarithmically subharmonic weighted Bergman space.
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