2024/03/08 by Calzi, Mattia
#31C10 #32M15 #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.2403.05436
Given a symmetric Siegel domain \mathscr D and a positive plurihamonic function f on \mathscr D, we study the largest positive Radon measure μ on the Silov boundary \mathrm b \mathscr D of \mathscr D whose Poisson integral \mathscr P μ is ≤ f. If \mathscr D has no tubular irreducible factors of rank ≥ 2, we show that \mathscr P μ is plurihamonic, and that f-\mathscr P μ is linear. As an application, we describe a possible analogue of the family of Clark measures associated with a holomorphic function from \mathscr D into the unit disc in \mathbb C.