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arXiv · 1503.03473

Characterizations of Symmetrized Polydisc

Sushil Gorai·Jaydeb Sarkar
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Abstract

Let $\Gamma_n$, $n \geq 2$, denote the symmetrized polydisc in $\mathbb{C}^n$, and $\Gamma_1$ be the closed unit disc in $\mathbb{C}$. We provide some characterizations of elements in $\Gamma_n$. In particular, an element $(s_1, \ldots, s_{n-1}, p) \in \mathbb{C}^n$ is in $\Gamma_n$ if and only if $s_j = \beta_j + \overline{\beta_{n-j}} p$, $j = 1, \ldots, n-1$, for some $(\beta_1, \ldots, \beta_{n-1}) \in \Gamma_{n-1}$, and $|p| \leq 1$.

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Sushil Gorai, Jaydeb Sarkar. 2015-03-11. Characterizations of Symmetrized Polydisc. https://arxiv.org/abs/1503.03473

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