Geodesic
Restoration of functions, integrals, and solutions to the heat conductivity equation from the Ulyanov $U_2$-classes
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 8 (2005) no. 4, pp. 337-351.

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper dealt with a problem of numerical integration, and approximate restoration of functions and solutions to the heat conductivity equation with functions of distribution of starting temperatures from the classes $U_2(\beta,\theta,\alpha)$ defined by the rate of decreasing the trigonometric Fourier coefficients. Optimal orders of errors of the quadrature formulas, restoration, and discretization by the trigonometric Fourier coefficients in $L_2$ and $L_{\infty}$ metrics are obtained. 
@article{SJVM_2005_8_4_a6,
     author = {Y. Y. Nurmoldin},
     title = {Restoration of functions, integrals, and solutions to the heat conductivity equation from the {Ulyanov} $U_2$-classes},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {337--351},
     publisher = {mathdoc},
     volume = {8},
     number = {4},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2005_8_4_a6/}
}
TY  - JOUR
AU  - Y. Y. Nurmoldin
TI  - Restoration of functions, integrals, and solutions to the heat conductivity equation from the Ulyanov $U_2$-classes
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2005
SP  - 337
EP  - 351
VL  - 8
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2005_8_4_a6/
LA  - ru
ID  - SJVM_2005_8_4_a6
ER  - 
%0 Journal Article
%A Y. Y. Nurmoldin
%T Restoration of functions, integrals, and solutions to the heat conductivity equation from the Ulyanov $U_2$-classes
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2005
%P 337-351
%V 8
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2005_8_4_a6/
%G ru
%F SJVM_2005_8_4_a6
Y. Y. Nurmoldin. Restoration of functions, integrals, and solutions to the heat conductivity equation from the Ulyanov $U_2$-classes. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 8 (2005) no. 4, pp. 337-351. http://geodesic.mathdoc.fr/item/SJVM_2005_8_4_a6/

[1] Temirgaliev N., “O zadache vosstanovleniya po netochnoi informatsii”, Vestnik Evraziiskogo natsionalnogo universiteta, 2004, no. 1, 202–209

[2] Lokutsievskii O. V., Gavrikov M. B., Nachala chislennogo analiza, TOO “Yanus”, M., 1995 | MR

[3] Magaril-Ilyaev G. G., Tikhomirov V. M., Vypuklyi analiz i ego prilozheniya, Izd. 2-e, ispravl., Editorial URSS, M., 2003

[4] Temirgaliev N., “Teoretiko-chislovye metody i teoretiko-veroyatnostnyi podkhod k zadacham analiza”, Vestnik ENU, 1997, no. 3, 90–144 ; “Теория вложений и приближений, абсолютная сходимость и преобразования рядов Фурье”, Вестник ЕНУ, 2002, No 3–4, 222–272 | MR

[5] Keipers L., Niderreiter G., Ravnomernoe raspredelenie posledovatelnostei, Nauka, M., 1985 | MR

[6] Korobov N. M., Teoretiko-chislovye metody v priblizhennom analize, Fizmatgiz, M., 1963 | MR | Zbl

[7] Hua Loo Keng, Wang Yuan, Application of Number Theory to Numerical Analysis, Springer, Berlin etc., 1981 | MR

[8] Sharygin I. F., “Otsenki snizu pogreshnosti kvadraturnykh formul na klassakh funktsii”, Zhurn. vychisl. matem. i mat. fiziki, 3 (1963), 370–376 | Zbl

[9] Ulyanov P. L., “O klassakh beskonechno differentsiruemykh funktsii”, Matem. sbornik, 181:5 (1990), 589–609

[10] Temirgaliev N., “Klassy $U_s(\beta,\theta,\alpha,\psi)$ i kvadraturnye formuly”, Dokl. RAN, 393:5 (2003), 605–608 | MR

[11] Kotlyar B. D., “O chisle tselykh tochek v ploskom mnozhestve”, Kvant, 1989, no. 10, 37

[12] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1977 | MR