Geodesic
On the asymptotics of the basic functions of a generalized Taylor series for some classes of infinitely differentiable functions
Dalʹnevostočnyj matematičeskij žurnal, Tome 11 (2011) no. 1, pp. 56-75

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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. 
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     author = {V. A. Makarichev},
     title = {On the asymptotics of the basic functions of a generalized {Taylor} series for some classes of infinitely differentiable functions},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {56--75},
     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2011_11_1_a5/}
}
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V. A. Makarichev. On the asymptotics of the basic functions of a generalized Taylor series for some classes of infinitely differentiable functions. Dalʹnevostočnyj matematičeskij žurnal, Tome 11 (2011) no. 1, pp. 56-75. http://geodesic.mathdoc.fr/item/DVMG_2011_11_1_a5/