Opuscula Mathematica
Opuscula Math. 35, no. 5 (), 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



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, .
Cite this article as:
Kunio Ichinobe, Masatake Miyake, On k-summability of formal solutions for certain partial differential operators with polynomial coefficients, Opuscula Math. 35, no. 5 (2015), 625-653, http://dx.doi.org/10.7494/OpMath.2015.35.5.625
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
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