Decomposition of solutions of the Cauchy problem of a quasi-homogeneous partial differential equation (Q435224)

Having the problem of the summability of formal solutions to the Cauchy problem of partial differential equations in mind, the authors discuss an explicit representation of formal solutions to the Cauchy problem of quasi-homogeneous partial differential equations with constant coefficients in the two-dimensional complex plane. The main result of the paper is an explicit decomposition formula for solutions, which is given in a form associated with the factorization of the relevant operators. This result can be regarded as a generalization of the decomposition formula for solutions to ordinary differential equations with constant coefficients.