Geodesic
Growth of norms in $L_2$ of derivatives of Steklov functions and properties of functions defined by best approximations and Fourier coefficients
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 31, Tome 445 (2016), pp. 5-32 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In the paper, for periodic functions, a connection between integrals of norms in $L_2$ of derivatives of Steklov functions and series constructed from Fourier coefficients and the best approximations in $L_2$ is established, and the question on their simultaneous convergence or divergence is considered. Similar investigations are carried out for even and odd periodic functions. 
@article{ZNSL_2016_445_a0,
     author = {M. V. Babushkin and V. V. Zhuk},
     title = {Growth of norms in $L_2$ of derivatives of {Steklov} functions and properties of functions defined by best approximations and {Fourier} coefficients},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--32},
     year = {2016},
     volume = {445},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_445_a0/}
}
TY  - JOUR
AU  - M. V. Babushkin
AU  - V. V. Zhuk
TI  - Growth of norms in $L_2$ of derivatives of Steklov functions and properties of functions defined by best approximations and Fourier coefficients
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2016
SP  - 5
EP  - 32
VL  - 445
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2016_445_a0/
LA  - ru
ID  - ZNSL_2016_445_a0
ER  - 
%0 Journal Article
%A M. V. Babushkin
%A V. V. Zhuk
%T Growth of norms in $L_2$ of derivatives of Steklov functions and properties of functions defined by best approximations and Fourier coefficients
%J Zapiski Nauchnykh Seminarov POMI
%D 2016
%P 5-32
%V 445
%U http://geodesic.mathdoc.fr/item/ZNSL_2016_445_a0/
%G ru
%F ZNSL_2016_445_a0
M. V. Babushkin; V. V. Zhuk. Growth of norms in $L_2$ of derivatives of Steklov functions and properties of functions defined by best approximations and Fourier coefficients. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 31, Tome 445 (2016), pp. 5-32. http://geodesic.mathdoc.fr/item/ZNSL_2016_445_a0/

[1] V. V. Zhuk, Approksimatsiya periodicheskikh funktsii, L., 1982 | MR

[2] P. L. Ulyanov, “O nekotorykh ekvivalentnykh usloviyakh skhodimosti ryadov i integralov”, UMN, 8:6(58) (1953), 133–141 | MR | Zbl

[3] P. L. Ulyanov, “O modulyakh nepreryvnosti i koeffitsientakh Fure”, Vestn. Mosk. un-ta. Matem. Mekhan., 1995, no. 1, 37–52 | MR | Zbl

[4] P. L. Ulyanov, “Ob ekvivalentnykh usloviyakh skhodimosti ryadov i integralov dlya trigonometricheskoi sistemy”, Dokl. RAN, 343:4 (1995), 458–462 | MR | Zbl

[5] N. K. Bari, Trigonometricheskie ryad, M., 1961

[6] M. K. Potapov, “K voprosu ob ekvivalentnosti uslovii skhodimosti ryadov Fure”, Mat. sb., 68(110):1 (1965), 111–127 | MR | Zbl

[7] M. K. Potapov, “O vlozhenii i sovpadenii nekotorykh klassov funktsii”, Izv. AN SSSR. Ser. mat., 33:4 (1969), 840–860 | MR | Zbl

[8] S. B. Stechkin, “O teoreme Kolmogorova–Seliverstova”, Izv. AN SSSR. Ser. mat., 17:6 (1953), 499–512 | MR | Zbl

[9] V. V. Zhuk, G. I. Natanson, Trigonometricheskie ryady Fure i elementy teorii approksimatsii, L., 1983 | MR

[10] B. Z. Vulikh, Kratkii kurs teorii funktsii veschestvennoi peremennoi, M., 1973

[11] V. K. Dzyadyk, Vvedenie v teoriyu ravnomernogo priblizheniya funktsii polinomami, M., 1977

[12] V. V. Zhuk, “Ob odnom metode summirovaniya ryadov Fure. Ryady Fure s polozhitelnymi koeffitsientami”, Issledovaniya po nekotorym problemam konstruktivnoi teorii funktsii, Sb. nauchn. trudov Leningr. mekh. in-ta, 50, 1965, 73–92

[13] V. V. Zhuk, “O priblizhenii $2\pi$-periodicheskoi funktsii lineinym operatorom”, Issledovaniya po nekotorym problemam konstruktivnoi teorii funktsii, Sb. nauchn. trudov Leningr. mekh. in-ta, 50, 1965, 93–115