arXiv subjects

Matěj Moravík

Publications and source records attributed to Matěj Moravík.

3 recordsLinked to original sources

arXiv2026

A Converse Mean-Value Property

We prove a converse mean-value theorem for harmonic functions associated with the invariant Laplace--Beltrami operator on the real unit ball. Under suitable integrability and topological assumptions on the domain and its Green potential, we show that the invariant volume mean-value property characterizes hyperbolic balls centered at the origin. As a consequence, we also answer a question left open by Bruna and Détraz in the setting of invariantly harmonic functions.

math.FA↗

arXiv2026

Analytic continuation of weighted $H$-harmonic Bergman spaces

We provide a partial answer to Problems 1 and 2 raised in the recent article by Blaschke et al., concerning the analytic continuation of weighted $H$-harmonic Bergman spaces. These are spaces of functions annihilated by the Möbius-invariant Laplacian on the unit ball. More precisely, we identify some of the discrete Wallach sets and show, among others, that structure depends on the parity of the dimension.

math.FA↗

arXiv2025

H-harmonic reproducing kernels on the ball

We consider the Szegő reproducing kernel associated with the space of $H$-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 Szegő kernel admits a representation as a finite sum of hypergeometric functions. We further show that the Szegő 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.

math.FA↗