Mathematics and Computer Science, Volume 2

26Estimating Error of Signals by Product Means (C, 2) of the Fourier Series in a W(L^r, ξ(t)) (r ≥ 1) Class

Pankaj Tiwari^⋆ and Aradhana Dutt Jauhari^†

Division of Mathematics, Department of Basic Sciences, Galgotias University, Greater Noida, G. B. Nagar, U.P., India

Abstract

The goal of this paper is to approach a new result on the degree of Fourier series approximation of a function g ∈ W(L^r, ξ(t))(r ≥ 1) class by product summability. Signals are handled as one-variable functions, while images are represented as two-variable functions. The concept’s research is directly tied to the rapidly developing field of information technology. The approximation theory is a trigonometric polynomial approximation. Many academics have researched in similar lines, but our research also proves some fresh findings.

Keywords: Degree of approximation, -means, weighted generalized lipschitz class, Fourier series, Lebesgue integral

26.1 Introduction

Let L = L(0, 2π) denote the space of 2π-periodic and Lebesgue integrable functions on the (0, 2π) Fourier series at point x:

Let ∑a_n be an nth partial sum ...