Far Eastern Mathematical Journal

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On the asymptotics of the basic functions of a generalized Taylor series for some classes of infinitely differentiable functions


V. A. Makarichev

2011, issue 1, Ñ. 56–75


Abstract
The existence of the asymptotics of the basic functions $\varphi_{s,n,k}(x)$ and \psi_{s,n,p}(x)$ of a generalized Taylor series for nonquasianalytic function class $H_{?,s}$ is proved. The first term of the asymptotic expansions of these functions is obtained.

Keywords:
nonquasianalytic class, generalized Taylor series, basic functions, atomic function

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References

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