An analogue of Polya's theorem for piecewise holomorphic functions. (December 2015)

• Record Type: Journal Article
• Authors: Buslaev, V. I.
• Is Part Of: Sbornik. Volume 206:Number 12(2015)
• Page Start: 1707
• Page End: 1721
• Publication Date: 2015-12
• Subjects: Primary 30C80 -- 31A15; rational approximations -- continued fractions -- Hankel determinants -- Padé approximants.; Mathematics -- Periodicals; 510.5
• DOI: 10.1070/SM2015v206n12ABEH004510
• Languages: English
• ISSNs: 1064-5616

Abstract

Abstract: A well-known result due to Polya for a function given by its holomorphic germ at is extended to the case of a piecewise holomorphic function on an arbitrary compact set in . 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.