MR2761091 Werner BALSER and Masafumi YOSHINO Werner BALSER and Masafumi YOSHINO Gevrey Order of Formal Power Series Solutions of Inhomogeneous Partial Differential Equations with Constant Coefficients Funkcialaj Ekvacioj. Serio Internacia 53 2010 411--434 http://fe.math.kobe-u.ac.jp/FE/FullPapers/53-3/53_411.pdf http://www.ams.org/mathscinet-getitem?mr=MR2761091 In an earlier paper, the first author showed that certain normalized formal solutions of homogeneous linear partial differential equations with constant coefficients are multisummable, with a multisummability type that can be determined from a Newton polygon associated with the PDE. In this article, some of the results obtained there are extended in several directions: First of all, arbitrary formal solutions of inhomogeous PDE are considered, and it is shown that, in some sense, they can be computed completely explicitly. Secondly, the Gevrey order of these formal solutions is determined. Finally, formal power series are discussed that, in general, do not satisfy a PDE with constant coefficients, but instead may be considered as solutions of singularly perturbed ODE, or integro-differential equations of a certain form. Moment summability, Moment-differential operator, Moment transformation, Gevrey order, Toeplitz operator. Primary 34M30; Secondary 34M25, 40G10. 53-411 2010 Gevrey Order of Formal Power Series Solutions of Inhomogeneous Partial Differential Equations with Constant Coefficients Werner BALSER and Masafumi YOSHINO Werner BALSER and Masafumi YOSHINO
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