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Properties of the Discrete Hilbert Transform

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Abstract

The asymptotic behavior of the distribution function of the Hilbert transform of sequences from the class l1 is studied. The concept of Q-summability of series is introduced; using this notion, it is shown that the Hilbert transform of a sequence from the class l1 is Q-summable and is Q-sum is zero.

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Acknowledgements

The authors are very grateful to the referee for many useful suggestions and comments that improved the original manuscript. The research of the first author was supported by the Science Development Foundation under the President of the Republic of Azerbaijan (Grant No. EIF/MQM/Elm-Tehsil-1-2016-1(26)-71/08/01).

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Authors and Affiliations

  1. Baku State University, 1148, Baku, Azerbaijan

    Rashid A. Aliev & Aynur F. Amrahova

  2. Institute of Mathematics and Mechanics, NAS of Azerbaijan, 1141, Baku, Azerbaijan

    Rashid A. Aliev

  3. Khazar University, 1096, Baku, Azerbaijan

    Aynur F. Amrahova

Authors
  1. Rashid A. Aliev
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  2. Aynur F. Amrahova
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Correspondence to Rashid A. Aliev.

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Communicated by Vladimir Bolotnikov.

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Aliev, R.A., Amrahova, A.F. Properties of the Discrete Hilbert Transform. Complex Anal. Oper. Theory 13, 3883–3897 (2019). https://doi.org/10.1007/s11785-019-00936-9

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