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Parametric Borel summability for some semilinear system of partial differential equations

Yamazawa H., Yoshino M.

Opuscula Mathematica

2015

Vol. 35, no. 5

825--845

In this paper we study the Borel summability of formal solutions with a parameter of first order semilinear system of partial differential equations with n independent variables. In [Singular perturbation of linear systems with a regular singularity, J. Dynam. Control. Syst. 8 (2002), 313-322], Balser and Kostov proved the Borel summability of formal solutions with respect to a singular perturbation parameter for a linear equation with one independent variable. We shall extend their results to a semilinear system of equations with general independent variables.

Approximation by means of Borel type of Fourier series

Tomczak K.

Fasciculi Mathematici

2002

Nr 33

115-123

In this paper we introduce and study approximation properties of means of the Borel type of Fourier series of functions belonging to the space C2pi.