On Hartman almost periodic functions

Guy Cohen, and Viktor Losert. "On Hartman almost periodic functions." Studia Mathematica 173.1 (2006): 81-101. <http://eudml.org/doc/285016>.

@article{GuyCohen2006,
abstract = {We consider multi-dimensional Hartman almost periodic functions and sequences, defined with respect to different averaging sequences of subsets in $ℝ^\{d\}$ or $ℤ^\{d\}$. We consider the behavior of their Fourier-Bohr coefficients and their spectrum, depending on the particular averaging sequence, and we demonstrate this dependence by several examples. Extensions to compactly generated, locally compact, abelian groups are considered. We define generalized Marcinkiewicz spaces based upon arbitrary measure spaces and general averaging sequences of subsets. We extend results of Urbanik to locally compact abelian groups.},
author = {Guy Cohen, Viktor Losert},
journal = {Studia Mathematica},
keywords = {Fourier-Bohr coefficients; Hartman almost periodic functions; generalized Besicovitch spaces; generalized Marcinkiewicz spaces; Følner sequences},
language = {eng},
number = {1},
pages = {81-101},
title = {On Hartman almost periodic functions},
url = {http://eudml.org/doc/285016},
volume = {173},
year = {2006},
}

TY - JOUR
AU - Guy Cohen
AU - Viktor Losert
TI - On Hartman almost periodic functions
JO - Studia Mathematica
PY - 2006
VL - 173
IS - 1
SP - 81
EP - 101
AB - We consider multi-dimensional Hartman almost periodic functions and sequences, defined with respect to different averaging sequences of subsets in $ℝ^{d}$ or $ℤ^{d}$. We consider the behavior of their Fourier-Bohr coefficients and their spectrum, depending on the particular averaging sequence, and we demonstrate this dependence by several examples. Extensions to compactly generated, locally compact, abelian groups are considered. We define generalized Marcinkiewicz spaces based upon arbitrary measure spaces and general averaging sequences of subsets. We extend results of Urbanik to locally compact abelian groups.
LA - eng
KW - Fourier-Bohr coefficients; Hartman almost periodic functions; generalized Besicovitch spaces; generalized Marcinkiewicz spaces; Følner sequences
UR - http://eudml.org/doc/285016
ER -