Geodesic
On the construction of approximations to continuous functions under integral boundary conditions
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 8, pp. 1370-1375 Cet article a éte moissonné depuis la source Math-Net.Ru

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On the basis of the resolvent of a simple differential operator, a method for finding approximations to continuous functions is constructed. In this method, both the approximated function and its approximations satisfy the given integral boundary condition 
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A. A. Khromov; G. V. Khromova. On the construction of approximations to continuous functions under integral boundary conditions. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 8, pp. 1370-1375. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_8_a1/

[1] Khromova G. V., “Priblizhayuschie svoistva rezolvent differentsialnykh operatorov v zadache priblizheniya funktsii i ikh proizvodnykh”, Zh. vychisl. matem. i matem. fiz., 38:7 (1998), 1106–1113 | MR | Zbl

[2] Khromov A. A., “Priblizhayuschie svoistva stepenei rezolventy operatora differentsirovaniya”, Izv. Saratovskogo un-ta. Ser. Matematika. Mekhanika. Informatika, 9:3 (2009), 75–78 | MR