Funkcialaj Ekvacioj
Print ISSN : 0532-8721
On Some Functional Equations with Borel Summable Solutions
Sunao Ōuchi
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2015 Volume 58 Issue 2 Pages 223-251

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Abstract
A functional equation Σmi=1aiui(z)) = f(z) is considered, where {φi(z)mi=1 are holomorphic functions in a neighborhood of z = 0 with φi(0) = 0 and f(z) is holomorphic in a sector with vertex z = 0. It is shown under some conditions of {φi(z)mi=1, f(z) and {ai}mi=1 that the equation has a formal power series solution that is Borel summable.
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© 2015 by the Division of Functional Equations, The Mathematical Society of Japan
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