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1980•Proceedings of the Japan Academy Series A Mathematical SciencesOpen access

Ultradifferentiability of solutions of ordinary differential equations

Hikosaburo Komatsu

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Abstract

Let M, p-0, 1, 2, ..., be a sequence of positive numbers.An in- finitely differentiable function f on an open set/2 in R is said to be an ultradifferentiable function of class {M} (resp. of class (M)) if or each compact set K in /2 there are constants h and C (resp. and 2or each h0 there is a constant C) such that sup ID"f(x)l=Chl"lMl,1,We assume that M satisfies the ollowing conditions"(1) M0=M=I;( 2 ) (M/q !)/-<(M/p .t)/-)2<qp, and furthermore in case of class (M) (3) p (ij (i) p=l, 2,...,

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Let M, p-0, 1, 2, ..., be a sequence of positive numbers.An in- finitely differentiable function f on an open set/2 in R is said to be an ultradifferentiable function of class {M} (resp. of class (M)) if or each compact set K in /2 there are constants h and C (resp. and 2or each h0 there is a constant C) such that sup ID"f(x)l=Chl"lMl,1,We assume that M satisfies the ollowing conditions"(1) M0=M=I;( 2 ) (M/q !)/-<(M/p .t)/-)2<qp, and furthermore in case of class (M) (3) p (ij (i) p=l, 2,...,

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Available abstract

Let M, p-0, 1, 2, ..., be a sequence of positive numbers.An in- finitely differentiable function f on an open set/2 in R is said to be an ultradifferentiable function of class {M} (resp. of class (M)) if or each compact set K in /2 there are constants h and C (resp. and 2or each h0 there is a constant C) such that sup ID"f(x)l=Chl"lMl,1,We assume that M satisfies the ollowing conditions"(1) M0=M=I;( 2 ) (M/q !)/-<(M/p .t)/-)2<qp, and furthermore in case of class (M) (3) p (ij (i) p=l, 2,...,

Key concepts: Ordinary differential equation, Mathematics, Applied mathematics, Differential equation, Mathematical analysis

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