H-harmonic reproducing kernels on the ball
Functional Analysis
2025-10-15 v1
Abstract
We consider the Szeg\H{o} reproducing kernel associated with the space of -harmonic functions on the unit ball in n-dimensional space, i.e. functions that are characterized by being annihilated by the hyperbolic Laplacian. This paper derives an explicit series expansion for the reproducing kernel in terms of a triple hypergeometric function introduced of Exton. Moreover, we demonstrate that the Szeg\H{o} kernel admits a representation as a finite sum of hypergeometric functions. We further show that the Szeg\H{o} kernel, for linearly dependent arguments, can be expressed in terms of the first Appell hypergeometric function. In addition we provide a series expansion for the weighted Bergman kernels.
Cite
@article{arxiv.2510.11821,
title = {H-harmonic reproducing kernels on the ball},
author = {Matěj Moravík},
journal= {arXiv preprint arXiv:2510.11821},
year = {2025}
}