Abstract
Polynomial spaces associated to a convex body C in \((\mathbb{R}^{+})^d\) 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 VC,K for \(K\subset \mathbb{C}^d\) 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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The first named author was supported by Simons Foundation Grant 707450.
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Levenberg, N., Wielonsky, F. Polynomials associated to non-convex bodies. Acta Math. Hungar. 165, 415–449 (2021). https://doi.org/10.1007/s10474-021-01188-w
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DOI: https://doi.org/10.1007/s10474-021-01188-w