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arXiv · 2104.03396

Polynomials associated to non-convex bodies

N. Levenberg·F. Wielonsky
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Abstract

Polynomial spaces associated to a convex body $C$ in $({\bf R}^+)^d$ have been the object of recent studies. In this work, we consider polynomial spaces associated to non-convex $C$. We develop some basic pluripotential theory including notions of $C-$extremal plurisubharmonic functions $V_{C,K}$ for $K\subset {\bf C}^d$ compact. Using this, we discuss Bernstein-Walsh type polynomial approximation results and asymptotics of random polynomials in this non-convex setting.

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N. Levenberg, F. Wielonsky. 2021-04-07. Polynomials associated to non-convex bodies. https://arxiv.org/abs/2104.03396

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