# Recovery of the functions of two variables with preservation of the class Cr(R2) with the help of their traces and the traces of their derivatives up to a fixed order on the given curve

 Title Recovery of the functions of two variables with preservation of the class Cr(R2) with the help of their traces and the traces of their derivatives up to a fixed order on the given curve Publication Type Journal Article Year of Publication 2014 Authors Lytvyn, OM, Lytvyn, OO, Tkachenko, OV, Gritsay, OL Abbreviated Key Title Dopov. Nac. akad. nauk Ukr. DOI 10.15407/dopovidi2014.02.050 Issue 2 Section Information Science and Cybernetics Pagination 50-55 Date Published 2/2014 Language Ukrainian Abstract The methods of construction of the operators of recovery of differentiable functions of two variables in a vicinity of the smooth curve, which preserve the class of differentiability $C^{r} (R^{2})$, are studied. The methods use the traces of an approximated function and its partial derivatives with respect to one variable up to a given order on the given curve. Keywords preservation of the class Cr(R2), recovery of the functions
References:

1. Sergiyenko I. V., Deineka V. V. System analysis. Kyiv: Nauk. dumka, 2013 (in Ukrainian).
2. Sergiyenko I. V., Zadiraka V. K., Lytvyn O. M. Elements of general theory of optimal algorithms and related matters. Kyiv: Nauk. dumka, 2012 (in Ukrainian).
3. Nikolsky S. M. Approximation of functions of several variables and imbedding theorems. Moscow: Nauka, 1969 (in Russian).
4. Besov O. V., Ilin V. P., Nikolsky S. M. Integral representations of functions and imbedding theorems. Moscow: Nauka, 1975 (in Russian).
5. Stein I. Singular integrals and differential properties of functions. Moscow: Mir, 1973 (in Russian).
6. Vladimirov V. S. Generalized functions in mathematical physics. Moscow: Nauka, 1979 (in Russian).
7. Khermander L. Differential operators with constant coefficients. Moscow: Mir, 1986 (in Russian).
8. Tikhonov A. N., Samarsky A. A. Equations of mathematical physics. Moscow: Nauka, 1966 (in Russian).
9. Shylov G. E. Mathematical analysis. The second special course. Moscow: Nauka, 1965 (in Russian).
10. Kvasov B. I. Methods of iso-geometric approximation by splines. Moscow: Fizmatlit, 2006 (in Russian).
11. Vinogradov I. M. (Ed.). Mathematical Encyclopedia. In 5 vols. Vol. 5. Moscow: Sov. entsyklopediia, 1984 (in Russian).
12. Lytvyn O. M. Dop. AN UkrSSR. Ser. A, 1984, No. 7: 15–19 (in Ukrainian).
13. Lytvyn O. M. Dop. AN UkrSSR. Ser. A, 1991, No. 3: 12-17 (in Ukrainian).
14. Lytvyn O. M. Dop. AN UkrSSR. Ser. A, 1987, No. 5: 13-17 (in Ukrainian).
15. Lytvyn O. M. Interlineation of the functions and some of its applications. Kharkiv: Osnova, 2002 (in Ukrainian).