Slawomir Michalik
Multisummability of formal solutions of inhomogeneous linear partial differential equations with constant coefficients
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ABSTRACT.  We consider the Cauchy problem for a general inhomogeneous linear partial differential equation with constant coefficients in two complex variables. We obtain necessary and sufficient conditions for the multisummability of formal solutions in terms of analytic continuation properties and growth estimates of some functions connected with the inhomogeneity. 
The results are presented in the general framework of $1/p$-fractional equations.