
Daghestan Electronic Mathematical Reports, 2017, Issue 7, Pages 29–39
(Mi demr34)




This article is cited in 1 scientific paper (total in 1 paper)
Sobolev orthogonal functions on the grid, generated by discrete orthogonal functions and the Cauchy problem for the difference equation
I. I. Sharapudinov^{ab}, Z. D. Gadzhieva^{ac}, R. M. Gadzhimirzaev^{a} ^{a} Daghestan Scientific Centre of Russian Academy of Sciences, Makhachkala
^{b} Vladikavkaz Scientific Centre of the Russian Academy of Sciences
^{c} Daghestan State Pedagogical University
Abstract:
We consider the system of functions ${\psi}_{r,n}(x)$ $(r=1,2,\ldots, n=0,1,\ldots)$ orthonormal on Sobolev with respect to the inner product of the form $\langle f,g\rangle=\sum_{k=0}^{r1}\Delta^kf(0)\Delta^kg(0)+
\sum_{j=0}^\infty\Delta^rf(j)\Delta^rg(j)\rho(j)$, generated by a given orthonormal system of functions ${\psi}_{n}(x)$ $( n=0,1,\ldots)$. It is shown that the Fourier series and Fourier sums by the system
${\psi}_{r,n}(x)$ $(r = 1,2, \ldots, n = 0,1, \ldots)$ are convenient and a very effective tool for the approximate solution of the Cauchy problem for difference equations.
Keywords:
Sobolev orthogonal functions, functions orthogonal on the grid, approximation of discrete functions, mixed series by the functions ortho\linebreak gonal on a uniform grid, iterative process for the approximate solution of difference equations
Funding Agency 
Grant Number 
Russian Foundation for Basic Research 
160100486a 
This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 160100486a) 
DOI:
https://doi.org/10.31029/demr.7.3
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UDC:
517.912 Received: 07.04.2017 Revised: 26.04.2017 Accepted:27.04.2017
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Citation:
I. I. Sharapudinov, Z. D. Gadzhieva, R. M. Gadzhimirzaev, “Sobolev orthogonal functions on the grid, generated by discrete orthogonal functions and the Cauchy problem for the difference equation”, Daghestan Electronic Mathematical Reports, 2017, no. 7, 29–39
Citation in format AMSBIB
\Bibitem{ShaGadGad17}
\by I.~I.~Sharapudinov, Z.~D.~Gadzhieva, R.~M.~Gadzhimirzaev
\paper Sobolev orthogonal functions on the grid, generated by discrete orthogonal functions and the Cauchy problem for the difference equation
\jour Daghestan Electronic Mathematical Reports
\yr 2017
\issue 7
\pages 2939
\mathnet{http://mi.mathnet.ru/demr34}
\crossref{https://doi.org/10.31029/demr.7.3}
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This publication is cited in the following articles:

M. S. Sultanakhmedov, “Cauchy problem for the difference equation and Sobolev orthogonal functions on the finite grid, generated by discrete orthogonal functions”, Dagestanskie elektronnye matematicheskie izvestiya, 2017, no. 7, 77–85

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