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

Abstract: We introduce new functional spaces that generalize the weighted Bergman and Dirichlet spaces on the disk D(0,R) in the complex plane and the Bargmann-Fock spaces on the whole complex plane. We give a complete description of the considered spaces. Mainly, we are interested in giving explicit formulas for their reproducing kernel functions and their asymptotic behavior as R goes to infinity.