On the existence of compacta of minimal capacity in the theory of rational approximation of multi-valued analytic functions

Viktor I. Buslaev; Sergey P. Suetin

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arXiv · 1505.06120

On the existence of compacta of minimal capacity in the theory of rational approximation of multi-valued analytic functions

Viktor I. Buslaev·Sergey P. Suetin

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Abstract

For an interval $E=[a,b]$ on the real line, let $μ$ be either the equilibrium measure, or the normalized Lebesgue measure of $E$, and let $V^μ$ denote the associated logarithmic potential. In the present paper, we construct a function $f$ which is analytic on $E$ and possesses four branch points of second order outside of $E$ such that the family of the admissible compacta of $f$ has no minimizing elements with regard to the extremal theoretic-potential problem, in the external field equals $V^{-μ}$.

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BibTeX RIS

Viktor I. Buslaev, Sergey P. Suetin. 2015-05-22. On the existence of compacta of minimal capacity in the theory of rational approximation of multi-valued analytic functions. https://arxiv.org/abs/1505.06120

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