Open AccessOn k-summability of formal solutions for certain partial differential operators with polynomial coefficients
Author(s) -
Kunio Ichinobe,
Masatake Miyake
Publication year - 2015
Publication title -
rocznik akademii górniczo-hutniczej im. stanisława staszica. opuscula mathematica/opuscula mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 16
eISSN - 2300-6919
pISSN - 1232-9274
DOI - 10.7494/opmath.2015.35.5.625
Subject(s) - mathematics , polynomial , pure mathematics , differential operator , discrete mathematics , combinatorics , mathematical analysis
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