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Multisummability of formal solutions of some linear partial differential equations. (English) Zbl 1020.35018
The author treats formal power series solutions \(\widetilde u(t,x)= \sum^\infty_{n=1} u_n(x)t^n\) of a linear partial differential equation in \(\mathbb{C}^{d+1}\) \[ P(t,x,\partial_t,\partial_x) u(t,x)=f(t,x),\;(t,x)\in \mathbb{C}\times \mathbb{C}^d. \] {}.

MSC:
35C10 Series solutions to PDEs
35A35 Theoretical approximation in context of PDEs
35F05 Linear first-order PDEs
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