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On the smoothness of slowly varying functions

Part of: Real functions

Published online by Cambridge University Press:  16 May 2024

Dalimil Peša Open the ORCID record for Dalimil Peša [Opens in a new window]
Dalimil Peša*
Affiliation:
Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Praha 8, Czech Republic
*
Email: [email protected]
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Abstract

In this paper, we consider the question of smoothness of slowly varying functions satisfying the modern definition that, in the last two decades, gained prevalence in the applications concerning function spaces and interpolation. We show that every slowly varying function of this type is equivalent to a slowly varying function that has continuous classical derivatives of all orders.

Keywords

slowly varying functionsapproximationsmoothness

MSC classification

Primary: 26A12: Rate of growth of functions, orders of infinity, slowly varying functions
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , First View , pp. 1 - 16
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.

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Footnotes

This research was supported by the Grant schemes at Charles University, reg. No. CZ.02.2.69/0.0/0.0/19_073/0016935, the grants no. P201/21-01976S and P202/23-04720S of the Czech Science Foundation and Charles University Research program No. UNCE/SCI/023.

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