Reproducing Properties of Holomorphic Kernels on Balls of ℂq

Abstract

In this work, we investigate the class of integral operators whose generating kernels have expansion series in terms of fundamental monomials. We study the reproducing kernel Hilbert space associated with such kernels, specifically when defined on balls about the origin of . Consequently, spectral properties, including the asymptotic behavior of the eigenvalues of these operators will be obtained. We also revisit our main results in the case in which the generating kernel is the Bergman kernel.