Uniform Approximation of the Curvature of Smooth Plane Curves with the Use of Partial Fourier Sums


Citar

Texto integral

Acesso aberto Acesso aberto
Acesso é fechado Acesso está concedido
Acesso é fechado Somente assinantes

Resumo

An error bound for the approximation of the curvature of graphs of periodic functions from the class Wr for r ≥ 3 in the uniform metric is obtained with the use of the simplest approximation technique for smooth periodic functions, which is approximation by partial sums of their trigonometric Fourier series. From the mathematical point of view, the interest in this problem is connected with the specific nonlinearity of the graph curvature operator on the class of smooth functions Wr on a period or a closed interval for r ≥ 2. There are several papers on curvature approximation for plane curves in the mean-square and Chebyshev norms. In previous works, the approximation was performed by partial sums of trigonometric series (in the L2 norm), interpolation splines with uniform knots, Fejér means of partial sums of trigonometric series, and orthogonal interpolating wavelets based on Meyer wavelets (in the C norm). The technique of this paper, based on the lemma, can possibly be generalized to the Lp metric and other approximation methods.

Sobre autores

Yu. Subbotin

Krasovskii Institute of Mathematics and Mechanics

Autor responsável pela correspondência
Email: yunsub@imm.uran.ru
Rússia, Yekaterinburg, 620990

N. Chernykh

Krasovskii Institute of Mathematics and Mechanics

Autor responsável pela correspondência
Email: Chernykh@imm.uran.ru
Rússia, Yekaterinburg, 620990

Arquivos suplementares

Arquivos suplementares
Ação
1. JATS XML

Declaração de direitos autorais © Pleiades Publishing, Ltd., 2018