Geodesic
A remark on indicator functions with gaps in the spectrum
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 108-115 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Developing a recent result of F. Nazarov and A. Olevskii, we show that for every subset $a$ of $\mathbb R$ of finite measure and every $\varepsilon>0$, there exists $b\subset\mathbb R$ with $|b|=|a|$ and $|(b\setminus a)\cup (a\setminus b)|\le\varepsilon$ such that the spectrum of $\chi_b$ is fairly thin. A generalization to locally compact Abelian groups is also provided. 
@article{ZNSL_2018_467_a9,
     author = {S. V. Kislyakov},
     title = {A remark on indicator functions with gaps in the spectrum},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {108--115},
     year = {2018},
     volume = {467},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a9/}
}
TY  - JOUR
AU  - S. V. Kislyakov
TI  - A remark on indicator functions with gaps in the spectrum
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2018
SP  - 108
EP  - 115
VL  - 467
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a9/
LA  - ru
ID  - ZNSL_2018_467_a9
ER  - 
%0 Journal Article
%A S. V. Kislyakov
%T A remark on indicator functions with gaps in the spectrum
%J Zapiski Nauchnykh Seminarov POMI
%D 2018
%P 108-115
%V 467
%U http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a9/
%G ru
%F ZNSL_2018_467_a9
S. V. Kislyakov. A remark on indicator functions with gaps in the spectrum. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 108-115. http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a9/

[1] F. Nazarov, A. Olevskii, “A function with support of finite measure and “small” spectrum”, 50 years with Hardy spaces, A tribute to Victor Havin, Operator theory: advances and applications, 261, Birkhäuser, Basel, 2018 | MR

[2] F. G. Arutyunyan, “Predstavlenie funktsii kratnymi ryadami”, Dokl. AN Arm.SSR, 64:2 (1977), 72–76 | MR | Zbl

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

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

[5] S. V. Kislyakov, “Ispravlenie do funktsii s redkim spektrom i ravnomerno skhodyaschimsya integralom Fure v sluchae gruppy $\mathbb R^n$”, Zap. nauchn. semin. POMI, 467, 2018, 116–127

[6] W. Rudin, Fourier analysis on groups, Interscience, New York–London, 1962 | MR | Zbl

[7] I. Stein, G. Veis, Vvedenie v garmonicheskii analiz na evklidovykh prostranstvakh, “Mir”, Moskva, 1974

[8] A. B. Aleksandrov, “Vnutrennie funktsii na kompaktnykh prostranstvakh”, Funkts. analiz i ego pril., 18:2 (1984), 1–13 | MR | Zbl

[9] S. V. Kislyakov, “Zamechaniya ob ‘ispravlenii’ ”, Zap. nauchn. semin. LOMI, 135, 1984, 69–75 | MR | Zbl