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

Aliev, Rashid A.; Amrahova, Aynur F.

Ural Math. J. 4, No. 2, 6-12 (2018).

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 \(l_1\).

MSC:

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

Keywords:

discrete Hilbert transform; asymptotic behavior of distribution function; class of summable sequences

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