Geodesic
Correction up to functions with sparce spectrum and uniformly convergent Fourier integral representation: the group $\mathbb R^n$
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 116-127 
S. V. Kislyakov. Correction up to functions with sparce spectrum and uniformly convergent Fourier integral representation: the group $\mathbb R^n$. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 116-127. http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a10/
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     author = {S. V. Kislyakov},
     title = {Correction up to functions with sparce spectrum and uniformly convergent {Fourier} integral representation: the group~$\mathbb R^n$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {116--127},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a10/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

This is an $\mathbb R^n$-conterpart of certain considerations on a similar subject for compact Abelian groups exposed by P. Ivanishvili and the author in 2010. The main difference with that paper is that certain notions and results of measure theory should be invoked in the case of $\mathbb R^n$.

[1] P. Ivanishvili, S. V. Kislyakov, “Ispravlenie do funktsii s redkim spektrom i ravnomerno skhodyaschimsya ryadom Fure”, Zap. nauchn. semin. POMI, 376, 2010, 25–47

[2] S. V. Kislyakov, “Novaya teorema ob ispravlenii”, Izv. AN SSSR. Ser. matem., 48:2 (1984), 305–330 | MR | Zbl

[3] A. B. Aleksandrov, “Spektralnye podprostranstva prostranstva $L^p$ pri $p1$”, Algebra i analiz, 19:3 (2007), 1–75 | MR | Zbl

[4] L. V. Kantorovich, G. P. Akilov, Funktsionalnyi analiz, Nauka, Moskva, 1977