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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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 $\mathbb R^n$. 
@article{ZNSL_2018_467_a10,
     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},
     year = {2018},
     volume = {467},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a10/}
}
TY  - JOUR
AU  - S. V. Kislyakov
TI  - Correction up to functions with sparce spectrum and uniformly convergent Fourier integral representation: the group $\mathbb R^n$
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2018
SP  - 116
EP  - 127
VL  - 467
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a10/
LA  - ru
ID  - ZNSL_2018_467_a10
ER  - 
%0 Journal Article
%A S. V. Kislyakov
%T Correction up to functions with sparce spectrum and uniformly convergent Fourier integral representation: the group $\mathbb R^n$
%J Zapiski Nauchnykh Seminarov POMI
%D 2018
%P 116-127
%V 467
%U http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a10/
%G ru
%F ZNSL_2018_467_a10
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/

[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