Some observations concerning polynomial convexity

Sushil Gorai

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arXiv · 1909.04094

Some observations concerning polynomial convexity

Sushil Gorai

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Abstract

In this paper we discuss a couple of observations related to polynomial convexity. More precisely, (i) We observe that the union of finitely many disjoint closed balls with centres in $\cup_{\theta\in[0,\pi/2]}e^{i\theta}V$ is polynomially convex, where $V$ is a Lagrangian subspace of $\mathbb{C}^n$. (ii) We show that any compact subset $K$ of $\{(z,w)\in\mathbb{C}^2: q(w)=\overline{p(z)}\}$, where $p$ and $q$ are two non-constant holomorphic polynomials in one variable, is polynomially convex and $\mathscr{P}(K)=\mathscr{C}(K)$.

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Sushil Gorai. 2019-09-09. Some observations concerning polynomial convexity. https://arxiv.org/abs/1909.04094

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