Issue |
E3S Web Conf.
Volume 515, 2024
International Scientific Conference Transport Technologies in the 21st Century (TT21C-2024) “Actual Problems of Decarbonization of Transport and Power Engineering: Ways of Their Innovative Solution”
|
|
---|---|---|
Article Number | 02010 | |
Number of page(s) | 7 | |
Section | Low Carbon Engineering | |
DOI | https://doi.org/10.1051/e3sconf/202451502010 | |
Published online | 12 April 2024 |
On a two-dimensional analogue of the Lebesgue function for Fourier-Chebyshov sums
Moscow State University of Civil Engineering (National Research University), 26, Yaroslavskoe Shosse, 129337, Moscow, Russia
* Corresponding author: aligadzhi@yandex.ru
This article considers the problem of approximating a function of two variables f(x,y) by Fourier sums over Chebyshev polynomials orthogonal on a discrete grid. The paper shows that if Tα,βn(x, N) (α,β > -1, n = 0,1,2,...) are classical Chebyshev polynomials, orthogonal on a discrete grid, then the system of polynomials of two variables {Zα,βm,n(x, y)}km,n=0 = {Tα,βm(x, N)}km,n=0, where k = m + n ≤ N −1 is orthogonal on the set ΩN × N = {(xi, yj)}i,j=1N - 1. For an arbitrary function f(x,y) continuous on [−1,1]2, partial Fourier Chebyshev sums Sα,βm,n,N(f, x,y) are constructed over the system of polynomials τα,βm,n,N(x,y) orthonormal on the grid ΩN × N = {(xi, yj)}i,j=1N - 1. The task is to estimate the partial sum Sα,βm,n,N(f, x,y) of the Fourier series of the function f(x,y) from the system of polynomials τα,βm,n,N(x,y) from the function itself f ∈ C[-1, 1]2, in the case when(x,y) ∈ [−1,1]×[−1,1], which in turn reduces to the problem of estimating the Lebesgue function Wα,βm,n,N(x,y). The result of the work is a theorem in which it is proved that the order of the Lebesgue constants ‖Sα,βm,n,N‖ of the indicated discrete sums under certain conditions is O((mn)q+1/2), where q = max{α,β}. As a consequence of the obtained result, some approximation properties of discrete sums Sα,βm,n,N(f, x,y) are considered.
© The Authors, published by EDP Sciences, 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.