Uniqueness of $H$-harmonic Moebius invariant inner products on the ball

TL;DR

This paper proves the uniqueness of the Moebius invariant semi-inner product for hyperbolic-harmonic functions on the unit ball in real n-space, establishing a fundamental property of these function spaces.

Contribution

It establishes the uniqueness of the Moebius invariant semi-inner product on hyperbolic-harmonic functions, a key aspect in understanding their structure and invariance properties.

Findings

Proves the uniqueness of the Moebius invariant semi-inner product.

Characterizes hyperbolic-harmonic functions on the unit ball.

Provides a foundational result for hyperbolic harmonic analysis.

Abstract

We~prove uniqueness of the Moebius invariant semi-inner product on hyperbolic-harmonic functions on the unit ball of the real n-space, i.e. on functions annihilated by the hyperbolic Laplacian on the ball.