Une densité sur un groupe abélien localement compact est un système borné de mesures cohérentes sur les quotients compacts de . Nous étudions l’algèbre de Banach des densités sur , en utilisant la théorie des fonctions presque périodiques comme moyen d’investigation principal. En particulier, nous caractérisons les groupes dans lesquels chaque densité est induite par une mesure sur le compactifié semi-périodique de . On donne des applications à la théorie d’équirépartition.
A density on a locally compact Abelian group is a bounded system of compatible measures on the compact quotients of . We study the Banach algebra of densities on , using the theory of almost periodic functions as a principal tool. In particular, we characterize those groups in which each density is induced by a measure on the semi-periodic compactification of . There are applications to the theory of uniform distribution.
@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}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {19}, number = {1}, year = {1969}, doi = {10.5802/aif.308}, mrnumber = {40 #3178}, zbl = {0176.11602}, language = {en}, url = {http://archive.numdam.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 - http://archive.numdam.org/articles/10.5802/aif.308/ DO - 10.5802/aif.308 LA - en ID - AIF_1969__19_1_81_0 ER -
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. http://archive.numdam.org/articles/10.5802/aif.308/
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