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

2024/04/29 by Bergur Snorrason, Snorrason, Bergur
Mathematics · #32A08 #32U15 (Secondary) #32U35 (Primary) #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Functional Equations Stability Results #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2404.18728

openalex publication_date 2024/04/29 · openalex created_date 2024/05/11 · openalex updated_date 2026/07/28

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.

Related

• Polynomials with exponents in compact convex sets and associated weighted extremal functions -- The Siciak-Zakharyuta theorem
• Polynomials with exponents in compact convex sets and associated weighted extremal functions -- Approximations and regularity
• The Siciak-Zahariuta extremal function as the envelope of disc functionals
• Polynomials with exponents in compact convex sets and associated weighted extremal functions -- Fundamental results
• Disc formulas for the weighted Siciak-Zahariuta extremal function