Hermitian interlineation of functions of two variables on the given system of disjoint lines with preservation of the class Cr (R2)

1Lytvyn, OM, 1Lytvyn, OO, 2Tkachenko, OV, 2Gritsay, OL
1Ukrainian Engineering Pedagogics Academy, Kharkiv
2Academician A.G. Ivchenko Zaporozhye Machine-Building Design Bureau Progress State Enterprise
Dopov. Nac. akad. nauk Ukr. 2014, 7:53-59
https://doi.org/10.15407/dopovidi2014.07.053
Section: Information Science and Cybernetics
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