Fractional cartesian products of sets
Annales de l'Institut Fourier, Volume 29 (1979) no. 2, p. 79-105

Let E be a subset of a discrete abelian group whose compact dual is G. E is exactly p-Sidon (respectively, exactly non-p-Sidon) when (*)C E (G) r holds if and only if r[p,] (respectively, r(p,)). E is said to be exactly Λ β (respectively, exactly non-Λ β ) if E has the property (**)everyfL E 2 (G)satisfies G exp (λ|f| 2/α <,forallλ>0, if and only if α[β,) (respectively, α(β,)).

In this paper, for every p[1,2) and β[1,), we display sets which are exactly p-Sidon, exactly non-p-Sidon, exactly Λ β and exactly non-Λ β .

Soit E un sous-ensemble du dual Γ d’un groupe compact G. On dit que E est exactement p-Sidon (resp. exactement non-p-Sidon) quand (*)C E (G) r si et seulement si r[p,] (resp. r(p,)). On dit que E est exactement Λ β (resp. exactement non-Λ β ) quand E vérifie (**)toute fL E 2 (G) est telle que, quel que soit λ>0,

G exp (λ|f|2/α<

si et seulement si α[β,) (resp. α(β,)).

Dans ce travail, pour chaque p[1,2) et β[1,), on construit des ensembles qui sont exactement p-Sidon, exactement non-p-Sidon, exactement Λ β et exactement non-Λ β .

@article{AIF_1979__29_2_79_0,
     author = {Blei, Ron C.},
     title = {Fractional cartesian products of sets},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {29},
     number = {2},
     year = {1979},
     pages = {79-105},
     doi = {10.5802/aif.744},
     zbl = {0381.43003},
     mrnumber = {81h:43008},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1979__29_2_79_0}
}
Blei, Ron C. Fractional cartesian products of sets. Annales de l'Institut Fourier, Volume 29 (1979) no. 2, pp. 79-105. doi : 10.5802/aif.744. http://www.numdam.org/item/AIF_1979__29_2_79_0/

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