On the summability of the discrete Hilbert transform. (English) Zbl 07255652

Summary: 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 \(l_1\).


47Bxx Special classes of linear operators
44Axx Integral transforms, operational calculus
47Axx General theory of linear operators
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