Hermitian interlineation of functions of two variables on the given system of disjoint lines with preservation of the class Cr (R2)
DOI:
https://doi.org/10.15407/dopovidi2014.07.053Keywords:
functions, Hermitian interlineation, preservation of the classAbstract
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 Cr (R2) 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.
Downloads
References
Sergienko I. V., Deineka V. S. System analysis of elastic and thermoelastic heterogeneous bodies. Kyiv: Nauk. dumka, 2012 (in Russian).
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).
Nikolskiy S. M. Approximation of functions of several variables and imbedding theorems. Moscow: Nauka, 1969 (in Russian).
Besov O. V., Ilin V. P., Nikolskiy S. M. Integral representations of functions and imbedding theorems. Moscow: Nauka, 1975 (in Russian).
Stein I. Singular integrals and differential properties of functions. Moscow: Mir, 1973 (in Russian).
Vladimirov V. S. C. Generalized functions in mathematical physics. Moscow: Nauka, 1979 (in Russian).
Hermander L. Differential operators with constant coefficients. Moscow: Mir, 1986 (in Russian).
Tikhonov A. N., Samarskiy A. A. Equations of mathematical physics. Moscow: Nauka, 1966 (in Russian).
Shylov G. E. Mathematical analysis. The second special course. Moscow: Nauka, 1965 (in Russian).
Kvasov B. I. The methods of iso-geometric approximation by splines. Moscow: Fizmatlit, 2006 (in Russian).
Vinogradova I. M. (Ed.). Mathematical encyclopedia. In 5th vols. Vol. 5.Moscow: Sov. entsyklopediia, 1984 (in Russian).
Lytvyn O. M. Dop. AN UkrRSR. Ser. A., 1984, No. 7: 15–19 (in Ukrainian).
Lytvyn O. M. Dop. AN UkrRSR. Ser. A., 1991, No. 3: 12–17 (in Ukrainian).
Lytvyn O. M. Dop. AN UkrRSR. Ser. A., 1987, No. 5: 13–17 (in Ukrainian).
Lytvyn O. M. Interlineation of the functions and some of its applications. Kharkiv: Osnova, 2002 (in Ukrainian).
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Reports of the National Academy of Sciences of Ukraine

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.