Geodesic
An example of a “bad” function with “good” Fourier coefficients
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2014), pp. 51-53 
B. Ayanbayev. An example of a “bad” function with “good” Fourier coefficients. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2014), pp. 51-53. http://geodesic.mathdoc.fr/item/VMUMM_2014_5_a8/
@article{VMUMM_2014_5_a8,
     author = {B. Ayanbayev},
     title = {An example of a {\textquotedblleft}bad{\textquotedblright} function with {\textquotedblleft}good{\textquotedblright} {Fourier} coefficients},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {51--53},
     year = {2014},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2014_5_a8/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

An example of “bad” integrable function with “good” Fourier coefficients is constructed in the paper. This result generalizes one theorem of M. I. Dyachenko and S. Yu. Tikhonov.