no. 1
Densities on locally compact abelian groups
Annales de l'Institut Fourier, Tome 19 (1969) no. 1, pp. 81-107

A density on a locally compact Abelian group G is a bounded system of compatible measures on the compact quotients of G. We study the Banach algebra of densities on G, using the theory of almost periodic functions as a principal tool. In particular, we characterize those groups G in which each density is induced by a measure on the semi-periodic compactification of G. There are applications to the theory of uniform distribution.

Une densité sur un groupe abélien localement compact G est un système borné de mesures cohérentes sur les quotients compacts de G. Nous étudions l’algèbre de Banach des densités sur G, en utilisant la théorie des fonctions presque périodiques comme moyen d’investigation principal. En particulier, nous caractérisons les groupes G dans lesquels chaque densité est induite par une mesure sur le compactifié semi-périodique de G. On donne des applications à la théorie d’équirépartition.

@article{AIF_1969__19_1_81_0,
     author = {Berg, I. D. and Rubel, L. A.},
     title = {Densities on locally compact abelian groups},
     journal = {Annales de l'Institut Fourier},
     pages = {81--107},
     year = {1969},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {19},
     number = {1},
     doi = {10.5802/aif.308},
     zbl = {0176.11602},
     mrnumber = {40 #3178},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.308/}
}
TY  - JOUR
AU  - Berg, I. D.
AU  - Rubel, L. A.
TI  - Densities on locally compact abelian groups
JO  - Annales de l'Institut Fourier
PY  - 1969
SP  - 81
EP  - 107
VL  - 19
IS  - 1
PB  - Institut Fourier
PP  - Grenoble
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.308/
DO  - 10.5802/aif.308
LA  - en
ID  - AIF_1969__19_1_81_0
ER  - 
%0 Journal Article
%A Berg, I. D.
%A Rubel, L. A.
%T Densities on locally compact abelian groups
%J Annales de l'Institut Fourier
%D 1969
%P 81-107
%V 19
%N 1
%I Institut Fourier
%C Grenoble
%U https://aif.centre-mersenne.org/articles/10.5802/aif.308/
%R 10.5802/aif.308
%G en
%F AIF_1969__19_1_81_0
Berg, I. D.; Rubel, L. A. Densities on locally compact abelian groups. Annales de l'Institut Fourier, Tome 19 (1969) no. 1, pp. 81-107. doi: 10.5802/aif.308

[1] I.D. Berg, The conjugate space of the space of semi-periodic sequences, Michigan Math. J. 13 (1966), p. 293-297. | Zbl | MR

[2] I.D. Berg, M. Rajagopalan and L.A. Rubel, Uniform distribution on locally compact Abelian groups, Trans. Amer. Math. Soc. 133 (1968) p. 435-446. | Zbl | MR

[3] R.C. Buck, The measure theoretic approach to density, Amer. J. Math. 68 (1946), p. 560-580. | Zbl | MR

[4] J. Cigler, Folgen normierter Masse auf kompakten Gruppen, Z. Wahrscheinlichkeitstheorie 1 (1962) p. 3-13. | Zbl | MR

[5] E. Hewitt and K.A. Ross, Abstract Harmonic Analysis, Springer Verlag, Berlin, (1963).

[6] L.A. Rubel, Uniform distribution in locally compact Abelian groups, Comm. Math. Helv. 93 (1965), p. 253-258. | Zbl | MR

[7] W. Rudin, Fourier Analysis in Groups, Interscience Publishers, (1962), New-York. | Zbl | MR

Cité par Sources :