Abstract
We study the k-summability of divergent formal solutions to the Cauchy problem for a class of linear partial differential operators of higher order with respect to t which have polynomial coefficients in t. We obtain a sufficient condition for the k-summability of formal solutions in terms of a global analyticity and a proper exponential growth estimate of the Cauchy data.
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Acknowledgements
The author is most grateful to the referees for their careful reading and kind comments and suggestions to improve this paper. The author is partially supported by the Grant-in-Aid for Scientific Research No. 15K04898 of Japan Society for the Promotion of Science.
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Ichinobe, K. (2017). On k-Summability of Formal Solutions for Certain Higher Order Partial Differential Operators with Polynomial Coefficients. In: Filipuk, G., Haraoka, Y., Michalik, S. (eds) Analytic, Algebraic and Geometric Aspects of Differential Equations. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-52842-7_9
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DOI: https://doi.org/10.1007/978-3-319-52842-7_9
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