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arXiv · 2404.18728

Polynomials with exponents in compact convex sets and associated weighted extremal functions -- Generalized product property

Bergur Snorrason
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Abstract

A famous result of Siciak is how the Siciak-Zakharyuta functions, sometimes called global extremal functions or pluricomplex Green functions with a pole at infinity, of two sets relate to the Siciak-Zakharyuta function of their cartesian product. In this paper Siciak's result is generalized to the setting of Siciak-Zakharyuta functions with growth given by a compact convex set, along with discussing why this generalization does not work in the weighted setting.

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Bergur Snorrason. 2024-04-29. Polynomials with exponents in compact convex sets and associated weighted extremal functions -- Generalized product property. https://doi.org/10.7146/math.scand.a-147788

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