On the theorem of Ivasev-Musatov. II
Annales de l'Institut Fourier, Volume 28 (1978) no. 3, p. 123-142
As in Part I [Annales de l’Inst. Fourier, 27-3 (1997), 97-113], our object is to construct a measure whose support has Lebesgue measure zero, but whose Fourier transform drops away extremely fast.
Comme dans la première partie [Annales de l’Inst. Fourier, 27-3 (1997), 97-113], il s’agit de construire une mesure portée par un compact de mesure de Lebesgue nulle, mais dont la transformée de Fourier tende vers zéro à l’infini aussi vite que possible. 
@article{AIF_1978__28_3_123_0,
     author = {Korner, Thomas-William},
     title = {On the theorem of Ivasev-Musatov. II},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {28},
     number = {3},
     year = {1978},
     pages = {123-142},
     doi = {10.5802/aif.705},
     zbl = {0368.28005},
     mrnumber = {80a:42005},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1978__28_3_123_0}
}

Korner, Thomas-William. On the theorem of Ivasev-Musatov. II. Annales de l'Institut Fourier, Volume 28 (1978) no. 3, pp. 123-142. doi : 10.5802/aif.705. http://www.numdam.org/item/AIF_1978__28_3_123_0/

[1] T. W. Korner, On the Theorem of Ivašev-Musatov I, Annales de l'Institut Fourier, 27, 3 (1977), 97-115. | Numdam | MR 57 #3721 | Zbl 0353.28001