On almost periodicity defined via non-absolutely convergent integrals

Dariusz Bugajewski; Adam Nawrocki

Czechoslovak Mathematical Journal (2025)

  • Issue: 1, page 193-214
  • ISSN: 0011-4642

Abstract

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We investigate some properties of the normed space of almost periodic functions which are defined via the Denjoy-Perron (or equivalently, Henstock-Kurzweil) integral. In particular, we prove that this space is barrelled while it is not complete. We also prove that a linear differential equation with the non-homogenous term being an almost periodic function of such type, possesses a solution in the class under consideration.

How to cite

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Bugajewski, Dariusz, and Nawrocki, Adam. "On almost periodicity defined via non-absolutely convergent integrals." Czechoslovak Mathematical Journal (2025): 193-214. <http://eudml.org/doc/299907>.

@article{Bugajewski2025,
abstract = {We investigate some properties of the normed space of almost periodic functions which are defined via the Denjoy-Perron (or equivalently, Henstock-Kurzweil) integral. In particular, we prove that this space is barrelled while it is not complete. We also prove that a linear differential equation with the non-homogenous term being an almost periodic function of such type, possesses a solution in the class under consideration.},
author = {Bugajewski, Dariusz, Nawrocki, Adam},
journal = {Czechoslovak Mathematical Journal},
keywords = {almost periodic function in view of the Lebesgue measure; barrelled space; Bohr almost periodic function; Denjoy-Bochner almost periodic function; Denjoy-Perron integral; Henstock-Kurzweil integral; linear differential equation},
language = {eng},
number = {1},
pages = {193-214},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On almost periodicity defined via non-absolutely convergent integrals},
url = {http://eudml.org/doc/299907},
year = {2025},
}

TY - JOUR
AU - Bugajewski, Dariusz
AU - Nawrocki, Adam
TI - On almost periodicity defined via non-absolutely convergent integrals
JO - Czechoslovak Mathematical Journal
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 193
EP - 214
AB - We investigate some properties of the normed space of almost periodic functions which are defined via the Denjoy-Perron (or equivalently, Henstock-Kurzweil) integral. In particular, we prove that this space is barrelled while it is not complete. We also prove that a linear differential equation with the non-homogenous term being an almost periodic function of such type, possesses a solution in the class under consideration.
LA - eng
KW - almost periodic function in view of the Lebesgue measure; barrelled space; Bohr almost periodic function; Denjoy-Bochner almost periodic function; Denjoy-Perron integral; Henstock-Kurzweil integral; linear differential equation
UR - http://eudml.org/doc/299907
ER -

References

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