Graham Theorem on Bounded Symmetric Domains

Abstract

Graham Theorem on the unit ball $B_n$ in ${\mathbb{C}}^n$ states that every invariant harmonic function $u\in C^n({\overline{B}}_n)$ must be pluriharmonic in $B_n$. This rigidity phenomenon of Graham have been studied by many authors. 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.

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