On the theorem of Ivasev-Musatov. I
Annales de l'Institut Fourier, Volume 27 (1977) no. 3, pp. 97-115.

We give a new version of Ivasev-Musatov’s construction of a measure whose support has Lebesgue measure zero but whose Fourier transform drops away extremely rapidly.

On donne une version nouvelle de la construction par Ivasev-Musatov d’une mesure telle que son support ait une mesure de Lebesgue nulle, mais telle que sa transformée de Fourier décroisse très vite.

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Korner, Thomas-William. On the theorem of Ivasev-Musatov. I. Annales de l'Institut Fourier, Volume 27 (1977) no. 3, pp. 97-115. doi : 10.5802/aif.662. https://aif.centre-mersenne.org/articles/10.5802/aif.662/

[1] O.S. Ivašev-Musatov, On the Fourier-Stieljes coefficients of singular functions, Dokl. Akad. Nauk SSSR (N.S.), 82 (1952), 9-11. (Russian). | Zbl

[2] O.S. Ivašev-Musatov, On Fourier-Stieljes coefficients of singular functions, Izv. Akad. Nauk SSSR., Ser. Mat., 20 (1956), 179-196. (Russian). English translation in Amer. Math. Soc. Translations, Series 2, 10 (1958), 107-124. | Zbl

[3] O.S. Ivašev-Musatov, On the coefficients of trigonometric nul series, Izv. Akad. Nauk SSSR., Ser. Nat., 21 (1957), 559-578. (Russian). English translation in Amer. Math. Soc. Translations, Series 2, 14 (1960), 289-310. | MR | Zbl

[4] J.-P. Kahane and R. Salem, Ensembles Parfaits et Séries Trigonométriques, Hermann Paris (1963). | MR | Zbl

[5] A. Zygmund, Trigonometric Series, Vols. I. & II., Cambridge (1959). | Zbl

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