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

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.

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.

@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},
     pages = {97--115},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {27},
     number = {3},
     year = {1977},
     doi = {10.5802/aif.662},
     zbl = {0353.28001},
     mrnumber = {57 #3721},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.662/}
}
TY  - JOUR
AU  - Korner, Thomas-William
TI  - On the theorem of Ivasev-Musatov. I
JO  - Annales de l'Institut Fourier
PY  - 1977
SP  - 97
EP  - 115
VL  - 27
IS  - 3
PB  - Institut Fourier
PP  - Grenoble
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.662/
DO  - 10.5802/aif.662
LA  - en
ID  - AIF_1977__27_3_97_0
ER  - 
%0 Journal Article
%A Korner, Thomas-William
%T On the theorem of Ivasev-Musatov. I
%J Annales de l'Institut Fourier
%D 1977
%P 97-115
%V 27
%N 3
%I Institut Fourier
%C Grenoble
%U https://aif.centre-mersenne.org/articles/10.5802/aif.662/
%R 10.5802/aif.662
%G en
%F AIF_1977__27_3_97_0
Korner, Thomas-William. On the theorem of Ivasev-Musatov. I. Annales de l'Institut Fourier, Tome 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

Cité par Sources :