Fourier Transforms of Measures and Algebraic Relations on Their Supports
Annales de l'Institut Fourier, Volume 59 (2009) no. 4, p. 1291-1319

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

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

DOI : https://doi.org/10.5802/aif.2464
Classification:  42A16
Keywords: Convolution, Fourier series
@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},
publisher = {Association des Annales de l'institut Fourier},
volume = {59},
number = {4},
year = {2009},
pages = {1291-1319},
doi = {10.5802/aif.2464},
mrnumber = {2566961},
zbl = {1179.42004},
language = {en},
url = {http://www.numdam.org/item/AIF_2009__59_4_1291_0}
}

Körner, Thomas W. Fourier Transforms of Measures and Algebraic Relations on Their Supports. Annales de l'Institut Fourier, Volume 59 (2009) no. 4, pp. 1291-1319. doi : 10.5802/aif.2464. http://www.numdam.org/item/AIF_2009__59_4_1291_0/

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

[2] Kaufman, R. A functional method for linear sets, Israel J. Math., Tome 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, Tome 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., Tome 135 (2007) no. 12, pp. 3823-3832 | Article | MR 2341932 | Zbl 1135.42002

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