Given two arbitrary almost periodic functions, we prove that the existence of
a common open vertical strip $V$, where both functions assume the same set of
values on every open vertical substrip included in $V$, is a necessary and
sufficient condition for both functions to have the same region of almost
periodicity and to be $^*$-equivalent. This represents an improvement of
previous results and it settles the problem of Bohr's equivalence theorem not
having a converse.
Publié le : 2019-01-22
Classification:
Mathematics - Classical Analysis and ODEs,
Mathematics - Complex Variables,
Mathematics - Number Theory,
42A75, 30D20, 11J72, 11K60
@article{1901.07917,
author = {Righetti, M. and Sepulcre, J. M. and Vidal, T.},
title = {The equivalence principle for almost periodic functions},
journal = {arXiv},
volume = {2019},
number = {0},
year = {2019},
language = {en},
url = {http://dml.mathdoc.fr/item/1901.07917}
}
Righetti, M.; Sepulcre, J. M.; Vidal, T. The equivalence principle for almost periodic functions. arXiv, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/1901.07917/