caa a22 4500 475741617 CHVBK 20180406123501.0 cr unu---uuuuu 170329e20000301xx s 000 0 eng 10.1007/BF02676675 doi (NATIONALLICENCE)springer-10.1007/BF02676675 Sharapudinov I. Dagestan State Pedagogical University, USSR aut Approximation of discrete functions and Chebyshev polynomials orthogonal on the uniform grid [Elektronische Daten] [I. Sharapudinov] Let $$\bar \Omega $$ N+2m ={−m, −m+1, ..., −1, 0, 1, ...,N−1,N, ...,N−1+m}. The present paper is devoted to the approximation of discrete functions of the formf : $$\bar \Omega $$ N+2m → ℝ by algebraic polynomials on the grid Ω N ={0, 1, ...,N−1}. On the basis of two systems of Chebyshev polynomials orthogonal on the sets Ω N+m and Ω N , respectively, we construct a linear operatorY n+2m, N =Y n+2m, N (f), acting in the space of discrete functions as an algebraic polynomial of degree at mostn+2m for which the following estimate holds (x ε Ω N ): 1 $$|f(x) - \mathcal{Y}_{n + 2m,N} (f,x)| \leqslant c(m)z\Theta _{N,m} (x)\left[ {\frac{{x + 1}}{N}\left( {1 - \frac{x}{N}} \right)} \right]^{m/2 - 1/4} \frac{{E_{n + m[g,\ell _2 (\Omega _{N + m} )]} }}{{n^{m - 1/2} }}$$ whereE n+m[g,l 2(Ω N+m )] is the best approximation of the function 1 $$g(x) = g(x,m,N) = ((N - 1 + m)/2)^m \Delta ^{^m } f(x - m)$$ by algebraic polynomials of degree at mostn+m in the spacel 2 (Ω N+m ) and the function Θ N, α (x) depends only on the weighted estimate for the Chebyshev polynomialsτ k α,α (x, N). Kluwer Academic/Plenum Publishers, 2000 Chebyshev polynomial nationallicence approximation of discrete functions nationallicence weighted estimate nationallicence Fourier series nationallicence Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/3(2000-03-01), 389-397 0001-4346 67:3<389 2000 67 11006 https://doi.org/10.1007/BF02676675 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02676675 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Sharapudinov I. Dagestan State Pedagogical University, USSR aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/3(2000-03-01), 389-397 0001-4346 67:3<389 2000 67 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer