Graham type theorem on classical bounded symmetric domains

Abstract

Graham Theorem on the unit ball Bn in C n states that every invariant harmonic function u ∈ C n (Bn) must be pluriharmonic in Bn [4]. This rigidity phenomenon of Graham have been studied by many authors ( see, for examples, [6], [10], [11], etc.) In this paper, we prove that Graham theorem holds on classical bounded symmetric domains. Which include Type I domains, Type II domains, Type III domains III(n) with even n and some special Type IV domains.