Geodesic
An analogue of Polya's theorem for piecewise holomorphic functions
Sbornik. Mathematics, Tome 206 (2015) no. 12, pp. 1707-1721

Voir la notice de l'article provenant de la source Math-Net.Ru

A well-known result due to Polya for a function given by its holomorphic germ at $z=\infty$ is extended to the case of a piecewise holomorphic function on an arbitrary compact set in $\overline{\mathbb C}$. This result is applied to the problem of the existence of compact sets that have the minimum transfinite diameter in the external field of the logarithmic potential of a negative unit charge among all compact sets such that a certain multivalued analytic function is single-valued and piecewise holomorphic on their complement. Bibliography: 13 titles.
Keywords: rational approximations, continued fractions, Hankel determinants
Mots-clés : Padé approximants. 
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     title = {An analogue of {Polya's} theorem for piecewise holomorphic functions},
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V. I. Buslaev. An analogue of Polya's theorem for piecewise holomorphic functions. Sbornik. Mathematics, Tome 206 (2015) no. 12, pp. 1707-1721. http://geodesic.mathdoc.fr/item/SM_2015_206_12_a2/