Abstract
For a bounded domain G in the complex plane, we focus on the problem of maximizing the minimum on the boundary ∂G of (weighted) polynomials of degree n having all zeros in a set D ⊂ G. For arbitrary unit measures μ on ∂ G and weight w:= exp{U μ}, the n-th root asymptotics of
is considered and related to the existence and construction of an inverse balayage of μ on \(\overline D\), i.e. of a measure such that μ is its balayage when sweeping to ∂G.
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Götz, M. Maximin Polynomials and Inverse Balayage. Comput. Methods Funct. Theory 5, 135–141 (2005). https://doi.org/10.1007/BF03321090
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DOI: https://doi.org/10.1007/BF03321090