Classification of infinitely differentiable periodic functions

@article{Stepanets2008ClassificationOI,
  title={Classification of infinitely differentiable periodic functions},
  author={A. I. Stepanets and A. Serdyuk and A. L. Shidlich},
  journal={Ukrainian Mathematical Journal},
  year={2008},
  volume={60},
  pages={1982-2005}
}
The set $ \mathcal{D}^\infty $ of infinitely differentiable periodic functions is studied in terms of generalized $ \overline \psi $-derivatives defined by a pair $ \overline \psi = (\psi_1, \psi_2)$ of sequences ψ1 and ψ2. In particular, we establish that every function f from the set $ \mathcal{D}^\infty $ has at least one derivative whose parameters ψ1 and ψ2 decrease faster than any power function. At the same time, for an arbitrary function f ∈ $ \mathcal{D}^\infty $ different from a… Expand
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