Weighted Bergman-Dirichlet and Bargmann-Dirichlet spaces of order m in high dimensions

2015/06/22 by Fardi, Ayman El, Ghanmi, Allal, Intissar, Ahmed +1
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1506.06499

Abstract

We introduce and study a generalization of the classical weighted Bergman and Dirichlet spaces on the unit ball in high dimension, the Bergman-Dirichlet spaces. Their counterparts on the whole n-complex space, the Bargmann-Dirichlet spaces, are also introduced and studied. Mainly, we give a complete description of the considered spaces, including orthonormal basis and the explicit formulas for their reproducing kernel functions. Moreover, we investigate their asymptotic behavior when the curvature goes to 0.

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