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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

National Aerospace University "Kharkiv Aviation Institute"

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 $H_{\rho,2}$ is proved. The first term of the asymptotic expansions of these functions is obtained.

Key words: nonquasianalytic class, generalized Taylor series, basic functions, atomic function.

UDC: 517

MSC: 42A70

Received: 17.01.2011

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