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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2403.05436 |
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| _version_ | 1866910361078202368 |
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| author | Calzi, Mattia |
| author_facet | Calzi, Mattia |
| 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 $\mathbb C$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05436 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Positive Pluriharmonic Functions on Symmetric Siegel Domains Calzi, Mattia Complex Variables 32M15, 31C10 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 $\mathbb C$. |
| title | Positive Pluriharmonic Functions on Symmetric Siegel Domains |
| topic | Complex Variables 32M15, 31C10 |
| url | https://arxiv.org/abs/2403.05436 |