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}
}
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
4 Citations