Uniqueness theorems for mean periodic functions on complex hyperbolic spaces (Q1410398)

A classical theorem of \textit{F. John} [Math. Ann. 111, 541-559 (1935; Zbl 0012.25402)] states that if a function \(f\in C^\infty (B_R)\) (where \(B_R\) is the open ball of radius \(R\) in the \(n\)-dimensional real Euclidean space) is such that its integral on each sphere with radius \(r<R\) contained in \(B_R\) is zero, then \(f\) is identically zero in \(B_R\). The aim of the paper under review is to obtain an analog to John`s theorem for the classes of functions that are mean periodic on noncompact, two-point homogeneous spaces; the author focuses on the case of the complex hyperbolic space \(H^n(\mathbf C)\).