Siciak-Zahariuta extremal functions, analytic discs and polynomial hulls

2008/08/25 by Finnur Lárusson, Larusson, Finnur, Ragnar Sigurðsson +1
Mathematics · #Holomorphic and Operator Theory #Advanced Banach Space Theory #Analytic and geometric function theory

paper · pdf · doi:10.48550/arxiv.0808.3304

Abstract

We prove two disc formulas for the Siciak-Zahariuta extremal function of an arbitrary open subset of complex affine space. We use these formulas to characterize the polynomial hull of an arbitrary compact subset of complex affine space in terms of analytic discs. Similar results in previous work of ours required the subsets to be connected.

Related

• Siciak-Zahariuta extremal functions and polynomial hulls
• The Siciak-Zahariuta extremal function as the envelope of disc functionals
• Analytic Discs, Global Extremal Functions and Projective Hulls in Projective Space
• Disc formulas for the weighted Siciak-Zahariuta extremal function
• Polynomials with exponents in compact convex sets and associated weighted extremal functions -- Generalized product property