Fourier Transforms of Measures and Algebraic Relations on Their Supports
[Transformées de Fourier et relations algèbriques pour leurs supports]
Annales de l'Institut Fourier, Tome 59 (2009) no. 4, pp. 1291-1319.

Si la transformée de Fourier d’une mesure décroît rapidement alors le support ne satisfait que très peu des relations algèbriques.

We investigate the relation between the rate of decrease of a Fourier transform and the possible algebraic relations on its support.

DOI : https://doi.org/10.5802/aif.2464
Classification : 42A16
Mots clés : convolution, séries de Fourier
@article{AIF_2009__59_4_1291_0,
     author = {K\"orner, Thomas W.},
     title = {Fourier Transforms of Measures and Algebraic Relations on Their Supports},
     journal = {Annales de l'Institut Fourier},
     pages = {1291--1319},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {59},
     number = {4},
     year = {2009},
     doi = {10.5802/aif.2464},
     mrnumber = {2566961},
     zbl = {1179.42004},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.2464/}
}
Körner, Thomas W. Fourier Transforms of Measures and Algebraic Relations on Their Supports. Annales de l'Institut Fourier, Tome 59 (2009) no. 4, pp. 1291-1319. doi : 10.5802/aif.2464. http://www.numdam.org/articles/10.5802/aif.2464/

[1] Kahane, J. P. Some random series of functions, Second edition. Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 1985 no. 5 | MR 833073 | Zbl 0571.60002

[2] Kaufman, R. A functional method for linear sets, Israel J. Math., Volume 5 (1967), pp. 185-187 | Article | MR 236607 | Zbl 0156.37403

[3] Kaufman, R. Small subsets of finite Abelian groups, Annales de l’Institut Fourier, Volume 18 (1968), pp. 99-102 | Article | Numdam | MR 241532 | Zbl 0175.30501

[4] Körner, T. W. K Measures on independent sets, a quantitative version of a theorem of Rudin, Proc. Amer. Math. Soc., Volume 135 (2007) no. 12, pp. 3823-3832 | Article | MR 2341932 | Zbl 1135.42002

[5] Kuratowski, K. Topology, I, Academic Press, New York-London, Państwowe Wydawnictwo Naukowe, Warsaw, 1966 (Translated from the French by J. Jaworowski) | MR 217751 | Zbl 0158.40802