TY  - JOUR
ID  - Ichinobe2015
LB  - Ichinobe2015
AU  - Ichinobe, Kunio
AU  - Miyake, Masatake
TI  - On k-summability of formal solutions for certain partial differential operators with polynomial coefficients
ST  - On k-summability of formal solutions for certain partial differential operators with polynomial coefficients
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2015
VL  - 35
IS  - 5
SP  - 625
EP  - 653
DO  - http://dx.doi.org/10.7494/OpMath.2015.35.5.625
UR  - http://dx.doi.org/10.7494/OpMath.2015.35.5.625
AB  - 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.
KW  - \(k\)-summability
KW  - Cauchy problem
KW  - power series solutions
KW  - successive approximation
SN  - 1232-9274
ER  -