$\varepsilon $-Kronecker and $I_{0}$ sets in abelian groups, IV:
interpolation by non-negative measures
Studia Mathematica, Tome 177 (2006) no. 1, pp. 9-24
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
A subset $E$ of a discrete abelian group is a “Fatou–Zygmund interpolation
set” ($F\kern-.75pt ZI_0$ set) if every bounded Hermitian function
on $E$ is the restriction of the Fourier–Stieltjes transform of a
discrete, non-negative measure.We show that every infinite subset of a discrete abelian group contains an
$F\kern-.75pt ZI_0$ set of the same cardinality (if the group is
torsion free, a stronger interpolation property holds) and that $\varepsilon
$-Kronecker sets are $F\kern-.75pt ZI_0$ (with that
stronger interpolation property).
Keywords:
subset discrete abelian group fatou zygmund interpolation set kern set every bounded hermitian function restriction fourier stieltjes transform discrete non negative measure every infinite subset discrete abelian group contains kern set cardinality group torsion stronger interpolation property holds varepsilon kronecker sets kern stronger interpolation property
Affiliations des auteurs :
Colin C. Graham 1 ; Kathryn E. Hare 2
@article{10_4064_sm177_1_2,
author = {Colin C. Graham and Kathryn E. Hare},
title = {$\varepsilon ${-Kronecker} and $I_{0}$ sets in abelian groups, {IV:
} interpolation by non-negative measures},
journal = {Studia Mathematica},
pages = {9--24},
publisher = {mathdoc},
volume = {177},
number = {1},
year = {2006},
doi = {10.4064/sm177-1-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm177-1-2/}
}
TY - JOUR
AU - Colin C. Graham
AU - Kathryn E. Hare
TI - $\varepsilon $-Kronecker and $I_{0}$ sets in abelian groups, IV:
interpolation by non-negative measures
JO - Studia Mathematica
PY - 2006
SP - 9
EP - 24
VL - 177
IS - 1
PB - mathdoc
UR - http://geodesic.mathdoc.fr/articles/10.4064/sm177-1-2/
DO - 10.4064/sm177-1-2
LA - en
ID - 10_4064_sm177_1_2
ER -
%0 Journal Article
%A Colin C. Graham
%A Kathryn E. Hare
%T $\varepsilon $-Kronecker and $I_{0}$ sets in abelian groups, IV:
interpolation by non-negative measures
%J Studia Mathematica
%D 2006
%P 9-24
%V 177
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm177-1-2/
%R 10.4064/sm177-1-2
%G en
%F 10_4064_sm177_1_2
Colin C. Graham; Kathryn E. Hare. $\varepsilon $-Kronecker and $I_{0}$ sets in abelian groups, IV:
interpolation by non-negative measures. Studia Mathematica, Tome 177 (2006) no. 1, pp. 9-24. doi: 10.4064/sm177-1-2
Cité par Sources :