Opuscula Math. 35, no. 5 (2015), 625-653
http://dx.doi.org/10.7494/OpMath.2015.35.5.625

Opuscula Mathematica

# On k-summability of formal solutions for certain partial differential operators with polynomial coefficients

Kunio Ichinobe
Masatake Miyake

Abstract. We study the $$k$$-summability of divergent formal solutions for the Cauchy problem of certain linear partial differential operators with coefficients which are polynomial in $$t$$. We employ the method of successive approximation in order to construct the formal solutions and to obtain the properties of analytic continuation of the solutions of convolution equations and their exponential growth estimates.

Keywords: $$k$$-summability, Cauchy problem, power series solutions, successive approximation.

Mathematics Subject Classification: 35C10, 35G10, .

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• Kunio Ichinobe
• Department of Mathematics Education, Aichi University of Education, Japan
• Masatake Miyake
• Graduate School of Mathematics, Nagoya University, Japan
• Communicated by P.A. Cojuhari.
• Revised: 2014-06-03.
• Accepted: 2014-07-23.
• Published online: 2015-04-27.