# On some new criteria for infinite differentiability of periodic functions

@article{Stepanets2007OnSN,
title={On some new criteria for infinite differentiability of periodic functions},
author={O. Stepanets and A. Serdyuk and A. L. Shydlich},
journal={Ukrainian Mathematical Journal},
year={2007},
volume={59},
pages={1569-1580}
}
• Published 2007
• Mathematics
• Ukrainian Mathematical Journal
AbstractWe study the set $$\mathcal{D}^\infty$$ of infinitely differentiable periodic functions in terms of generalized $$\bar \psi$$-derivatives defined by a pair $$\bar \psi = (\psi _1 ,\psi _2 )$$ of sequences ψ1 and ψ2. It is shown that every function ƒ from the set $$\mathcal{D}^\infty$$ has at least one derivative whose parameters ψ1 and ψ2 decrease faster than any power function and, at the same time, for any function ƒ ∈ $$\mathcal{D}^\infty$$ different from a… Expand
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