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We introduce new functional spaces that generalize the weighted Bergman andDirichlet spaces on the disk D(0,R) in the complex plane and the Bargmann-Fockspaces on the whole complex plane. We give a complete description of theconsidered spaces. Mainly, we are interested in giving explicit formulas fortheir reproducing kernel functions and their asymptotic behavior as R goes toinfinity.

Weighted Bergman-Dirichlet and Bargmann-Dirichlet spaces of order $m$: Explicit formulae for reproducing kernels and asymptotic