Abstract
The purpose of this paper is to analyze the degree of approximation of a function \(\overline f\) that is a conjugate of a function \(f\) belonging to the Lipschitz class by Hausdorff means of a conjugate series of the Fourier series.
Highlights
The sequence of partial sums sn(x) for a conjugate series of the Fourier series of function f converges at the point x to the number f (x) = −1 2π π 0 f (x+t)−f (x−t) tan(t/2)dt if the function f at the point x satisfies the Lipschitz condition |f (x ± t) − f (x)| < Ctα for α ∈
If we assume the degree of approximation supx∈R |sn(x) − f (x)|, the following question arises: does the sequence (n + 1)α supx∈R |sn(x) − f (x)|
Several studies have been conducted on the degree of approximation of a function by different summability means of its Fourier series
Summary
The degree of approximation by Hausdorff means of a conjugate Fourier series Abstract. The purpose of this paper is to analyze the degree of approximation of a function f that is a conjugate of a function f belonging to the Lipschitz class by Hausdorff means of a conjugate series of the Fourier series
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