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On the summability of formal solutions of linear partial differential equations. (English) Zbl 1085.35043
Linear partial differential equations (PDEs) with holomorphic coefficients are under consideration. The goal of the paper is to provide a general approach to the construction of Borel summable formal series solution of above mentioned PDEs. Sufficient conditions for the existence and uniqueness of formal series in variable \(t\) are given, and the \(k\)-summability properties of these formal series are investigated.

MSC:
35C10 Series solutions to PDEs
35C20 Asymptotic expansions of solutions to PDEs
40G10 Abel, Borel and power series methods
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