On the degree of continuity and smoothness of sine and cosine Fourier transforms of Lebesgue integrable functions

Móricz, Ferenc

doi:10.1007/s10474-011-0167-2

Cited by 1 publication

(1 citation statement)

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“…Over the years, many investigators [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] have investigated the approximation of 2𝜋-periodic functions of two variables from various Lipschitz and Zygmund classes using different summability techniques. The first result was given by Chow [3] in 1954, who used the Cesàro summability of the double Fourier series.…”

Section: Introductionmentioning

confidence: 99%

Approximation by double matrix means of bivariate functions belonging to weighted Lipschitz and Zygmund classes

Devaiya,

Srivastava

2023

Math Methods in App Sciences

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This study focuses on the rate of uniform approximation for continuous functions ‐periodic in each variable, using double matrix means of the rectangular partial sums of double Fourier series. The importance of the weighted integral modulus of symmetric smoothness lies in its ability to capture the local behavior of a function. So we obtain the results in terms of the weighted integral modulus of symmetric smoothness. In addition, we introduce the concept of the weighted Lipschitz and Zygmund classes as an extension of the existing Lipschitz classes and and Zygmund classes and , respectively. These weighted classes allow us a more detailed analysis of the approximation rates of functions by assigning the weights to different regions of the domain of function. Further, we prove two theorems about the degree (error) of approximation of functions belonging to these classes using double matrix means. We also discuss some corollaries from our results.

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