ON THE SUMMABILITY OF THE DISCRETE HILBERT TRANSFORM

Abstract

In this paper, we study the asymptotic behavior of the distribution function of the discrete Hilbert transform of sequences from the class \(l_{1} \) and find a necessary condition and a sufficient condition for the summability of the discrete Hilbert transform of a sequence from the class \(l_{1} \).

Keywords

• Discrete Hilbert transform, Asymptotic behavior of the distribution function, Class of summable sequences