# 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}
}
• Published 2008
• Mathematics
• Ukrainian Mathematical Journal
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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