Title  Hermitian interlineation of functions of two variables on the given system of disjoint lines with preservation of the class C^{r} (R^{2}) 
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/dopovidi2014.07.053 
Issue  7 
Section  Information Science and Cybernetics 
Pagination  5359 
Date Published  7/2014 
Language  Ukrainian 
Abstract  Methods for constructing the operators of a Hermitian interlineation of the recovery of differentiable functions of two variables on the system of smooth disjoint curves that preserve the class of differentiability $C^{r}$ ($\mathbb{R}^{2})$ are studied. To construct these operators, the traces of the interpolated function and its partial derivatives with respect to one variable to a given order on the mentioned system of curves are used.

Keywords  functions, Hermitian interlineation, preservation of the class 
1. Sergienko I. V., Deineka V. S. System analysis of elastic and thermoelastic heterogeneous bodies. Kyiv: Nauk. dumka, 2012 (in Russian).
2. Sergienko I. V., Zadiraka V. K., Lytvyn O. M. Elements of the General theory of optimal algorithms and related matters. Kyiv: Nauk. dumka, 2012 (in Ukrainian).
3. Nikolskiy S. M. Approximation of functions of several variables and imbedding theorems. Moscow: Nauka, 1969 (in Russian).
4. Besov O. V., Ilin V. P., Nikolskiy 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. C. Generalized functions in mathematical physics. Moscow: Nauka, 1979 (in Russian).
7. Hermander L. Differential operators with constant coefficients. Moscow: Mir, 1986 (in Russian).
8. Tikhonov A. N., Samarskiy 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. The methods of isogeometric approximation by splines. Moscow: Fizmatlit, 2006 (in Russian).
11. Vinogradova I. M. (Ed.). Mathematical encyclopedia. In 5th vols. Vol. 5.Moscow: Sov. entsyklopediia, 1984 (in Russian).
12. Lytvyn O. M. Dop. AN UkrRSR. Ser. A., 1984, No. 7: 15–19 (in Ukrainian).
13. Lytvyn O. M. Dop. AN UkrRSR. Ser. A., 1991, No. 3: 12–17 (in Ukrainian).
14. Lytvyn O. M. Dop. AN UkrRSR. 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).