On Some Functional Equations with Borel Summable Solutions

抄録

A functional equation Σ^m_i=1a_iu(φ_i(z)) = f(z) is considered, where {φ_i(z)^m_i=1 are holomorphic functions in a neighborhood of z = 0 with φ_i(0) = 0 and f(z) is holomorphic in a sector with vertex z = 0. It is shown under some conditions of {φ_i(z)^m_i=1, f(z) and {a_i}^m_i=1 that the equation has a formal power series solution that is Borel summable.