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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.05436 |
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Table of Contents:
- 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 $\leq f$. If $\mathscr D$ has no tubular irreducible factors of rank $\geq 2$, 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 $\mathbb C$.