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Some results on spherical approximation
Author(s) -
Fragoulopoulou M.,
Nestoridis V.,
Papadoperakis I.
Publication year - 2013
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdt047
Subject(s) - mathematics , disjoint sets , bounded function , real line , metric (unit) , finite set , set (abstract data type) , line (geometry) , type (biology) , pure mathematics , discrete mathematics , mathematical analysis , geometry , ecology , operations management , computer science , economics , biology , programming language
We extend Mergelyan's theorem to the case of compact sets K ⊂ℂ bounded by a finite number of disjoint Jordan curves, where the approximation is uniform with respect to the chordal metric χ and it is realized by rational functions with prescribed poles off K . Allowing poles in K °, as well, we obtain an analog result with the only assumption that K c has a finite number of components. We also obtain a Runge's‐type result and we introduce the notion of χ‐Arakelian sets in ℂ. In this respect, we prove that the real line is such a set.