Multisummability of formal power series solutions of partial differential equations with constant coefficients |
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Authors: | Werner Balser |
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Institution: | Abteilung Angewandte Analysis, Abteilung Mathematik V, Universität Ulm, Ulm 89069, Germany |
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Abstract: | In an earlier paper of the author's, partial differential equations with constant coefficients have been studied. Under a certain (restrictive) assumption upon the equation, those initial conditions were characterized for which the normalized formal solution of a corresponding Cauchy problem is k-summable. Here we treat the general situation and prove an analogous result, using multisummability instead of k-summability. The appropriate multisummability type is shown to depend upon the given PDE only, and can be determined from a corresponding Newton polygon. |
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Keywords: | 35C10 35C20 |
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