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 
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/
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     title = {Restoration of functions, integrals, and solutions to the heat conductivity equation from the {Ulyanov} $U_2$-classes},
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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.

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