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

@article{AIF_1977__27_3_97_0,
     author = {Korner, Thomas-William},
     title = {On the theorem of Ivasev-Musatov. I},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {27},
     number = {3},
     year = {1977},
     pages = {97-115},
     doi = {10.5802/aif.662},
     zbl = {0353.28001},
     mrnumber = {57 \#3721},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1977__27_3_97_0}
}
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. http://www.numdam.org/item/AIF_1977__27_3_97_0/

[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 0046.06703

[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 0093.07004

[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 20 #5392 | Zbl 0094.27101

[4] J.-P. Kahane and R. Salem, Ensembles Parfaits et Séries Trigonométriques, Hermann Paris (1963). | MR 28 #3279 | Zbl 0112.29304

[5] A. Zygmund, Trigonometric Series, Vols. I. & II., Cambridge (1959). | Zbl 0085.05601