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On finite sums of periodic functions

  • Alexander Kharazishvili EMAIL logo

Abstract

It is shown that any function acting from the real line into itself can be expressed as a pointwise limit of finite sums of periodic functions. At the same time, the real analytic function xexp(x2) cannot be represented as a uniform limit of finite sums of periodic functions and, simultaneously, this function is a locally uniform limit of finite sums of periodic functions. The latter fact needs the techniques of Hamel bases.

MSC 2010: 26A03; 26A12; 28A20

Award Identifier / Grant number: FR-18-6190

Funding statement: This work was supported by Shota Rustaveli National Science Foundation of Georgia (SRNSFG) Grant FR-18-6190.

Acknowledgements

The results of this paper were reported at the International Conference dedicated to the 120th anniversary of Professor K. Kuratowski (Lviv, September 27 – October 1, 2016).

References

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Received: 2016-08-08
Accepted: 2017-01-12
Published Online: 2020-01-17
Published in Print: 2020-06-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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