Geodesic
On approximation of functions by trigonometric polynomials with incomplete spectrum in $L_p$, $0$
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 37, Tome 366 (2009), pp. 67-83 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Suppose $B$ is a subset of integers that possesses certain arithmetic properties. Estimates of the best approximation of functions in the space $L_p$, $0, by trigonometric polynomials that are constructed by the system $\{e^{ikx}\}_{k\in\mathbb Z\setminus B}$ are obtained. Bibl. – 13 titles. 
@article{ZNSL_2009_366_a4,
     author = {Yu. S. Kolomoitsev},
     title = {On approximation of functions by trigonometric polynomials with incomplete spectrum in $L_p$, $0<p<1$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {67--83},
     year = {2009},
     volume = {366},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_366_a4/}
}
TY  - JOUR
AU  - Yu. S. Kolomoitsev
TI  - On approximation of functions by trigonometric polynomials with incomplete spectrum in $L_p$, $0
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2009
SP  - 67
EP  - 83
VL  - 366
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2009_366_a4/
LA  - ru
ID  - ZNSL_2009_366_a4
ER  - 
%0 Journal Article
%A Yu. S. Kolomoitsev
%T On approximation of functions by trigonometric polynomials with incomplete spectrum in $L_p$, $0
%J Zapiski Nauchnykh Seminarov POMI
%D 2009
%P 67-83
%V 366
%U http://geodesic.mathdoc.fr/item/ZNSL_2009_366_a4/
%G ru
%F ZNSL_2009_366_a4
Yu. S. Kolomoitsev. On approximation of functions by trigonometric polynomials with incomplete spectrum in $L_p$, $0

[1] A. A. Talalyan, “Predstavlenie funktsii klassov $L_p[0,1]$, $0

1$, ortogonalnymi ryadami”, Acta Math. Academ. Sci. Hungar., 21:1–2 (1970), 1–9 | DOI | Zbl

[2] J. H. Shapiro, “Subspaces of $L_p(G)$ spanned by characters: $0

1$”, Isr. J. Math., 29:2–3 (1978), 248–264 | DOI | MR | Zbl

[3] V. I. Ivanov, V. A. Yudin, “O trigonometricheskoi sisteme v $L_p$, $0

1$”, Mat. zametki, 28:6 (1980), 859–868 | MR | Zbl

[4] A. B. Aleksandrov, “Essays on non locally convex Hardy classes”, Lecture Notes in Math., 864, Springer-Verlag, 1981, 1–89 | DOI | MR

[5] V. I. Ivanov, “Predstavlenie izmerimykh funktsii kratnymi trigonometricheskimi ryadami”, Tr. MIAN SSSR, 164, 1983, 100–123 | Zbl

[6] Yu. S. Kolomoitsev, “Polnota trigonometricheskoi sistemy v klassakh $\varphi(L)$”, Mat. zametki, 81:5 (2007), 707–712 | DOI | MR | Zbl

[7] E. A. Storozhenko, V. G. Krotov, P. Osvald, “Pryamye i obratnye teoremy tipa Dzheksona v prostranstvakh $L_p$, $0

1$”, Matem. sb., 98(140):3 (1975), 395–415 | MR | Zbl

[8] V. I. Ivanov, “Pryamye i obratnye teoremy teorii priblizheniya v metrike $L_p$ dlya $0

1$”, Mat. zametki, 18:5 (1975), 641–658 | MR | Zbl

[9] K. V. Runovskii, “O semeistve lineinykh polinomialnykh operatorov v prostranstvakh $L_p$, $0

1$”, Matem. sb., 184:2 (1993), 33–42 | MR | Zbl

[10] R. M. Trigub, E. S. Belinsky, Fourier Analysis and Approximation of Functions, Kluwer, 2004 | Zbl

[11] E. A. Storozhenko, “Teoremy vlozheniya i nailuchshie priblizheniya”, Matem. sb., 97(139):2 (1975), 230–241 | MR | Zbl

[12] V. V. Peller, “Opisanie operatorov Gankelya klassa $\mathfrak S_p$ pri $p>0$, issledovanie skorosti ratsionalnoi approksimatsii i drugie prilozheniya”, Matem. sb., 122(164):4 (1983), 481–510 | MR | Zbl

[13] A. A. Bukhshtab, Teoriya chisel, Prosveschenie, M., 1966 | Zbl