Sets of multiplicity in locally compact abelian groups
Annales de l'Institut Fourier, Tome 16 (1966) no. 2, pp. 123-158.

Dans tout groupe abélien localement compact G, il existe une mesure de Radon dont la transformée de Fourier tend vers zéro à l’infini et dont le support engendre dans G un sous-groupe de mesure de Haar nulle.

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     author = {Varopoulos, Nicolas Th.},
     title = {Sets of multiplicity in locally compact abelian groups},
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     year = {1966},
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Varopoulos, Nicolas Th. Sets of multiplicity in locally compact abelian groups. Annales de l'Institut Fourier, Tome 16 (1966) no. 2, pp. 123-158. doi : 10.5802/aif.238. https://aif.centre-mersenne.org/articles/10.5802/aif.238/

[1] N. Bourbaki, Livre VI Integration.

[2] E. Hewitt, Michigan Math. J., 5, (1958), 149-158. | Zbl 0085.10003

[3] I. Kaplanski, Infinite Abelian Groups, The University of Michigan press.

[4] M. Loève, Probability Theory, Van Nostrand. | Zbl 0095.12201

[5] W. Rudin, Fourier Stieltjes transforms of measures on independant sets, Bull. Amer. Math. Soc., 66 (1960). | Zbl 0099.32201

[6] W. Rudin, Fourier analysis on groups, Interscience tract, 12. | MR 27 #2808 | Zbl 0107.09603

[7] R. Salem, On sets of multiplicity for trigonometric series, Amer. Journ. of Math., 64 (1942), 531-538. | MR 4,38b | Zbl 0060.18603

[8] N. Th. Varopoulos, The functions that operate on B0 (Г) of a discrete group, Bull. Soc. Math. France, 93 (1965) (to appear). | Numdam | Zbl 0139.30801

[9] N. Th. Varopoulos, Sur les mesures de Radon d'un groupe localement compact abélien, C.R. Acad. Sc. Paris, t. 260, 1059-1062 (1965). | Zbl 0134.12201

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