Differential systems of type \((1,1)\) on Hermitian symmetric spaces and their solutions. (Q1888369)

Symmetric spaces \(G/K\) carry many symmetric structures. One aspect is given by the rich structure of \(G\)-invariant differential operators. They are important for harmonic analysis on symmetric spaces. After classifying \(G\)-invariant systems of type (1,1) on a Hermitian symmetric space, this paper shows that for a particular system of type (1,1) containing the Laplace-Beltrami operator and the complementary Hua system, every bounded real-valued function on \(G/H\) is annhiliated by this system if and only if it is pluriharmonic. This completes the characterization of bounded functions which are annhiliated by any system of type (1,1) containing the Laplace-Beltrami operator.