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μ-Hankel operators on compact Abelian groups

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(μ; ν)-Hankel operators between separable Hilbert spaces were introduced and studied recently (A. Mirotin and E. Kuzmenkova, μ-Hankel operators on Hilbert spaces, Opuscula Math., 41 (2021), 881–899). This paper is devoted to generalization of (μ; ν)-Hankel operators to the case of (non-separable in general) Hardy spaces over compact and connected Abelian groups. In this setting bounded (μ; ν)-Hankel operators are fully described under some natural conditions. Examples of integral operators are also considered.

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Acknowledgement

The author thanks the referee for suggestions that essentially improve the presentation.

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Authors and Affiliations

  1. Department of Mathematics and Programming Technologies, Francisk Skorina Gomel State University, Gomel, 246019, Belarus

    A. Mirotin

  2. Regional Mathematical Center, Southern Federal University, Rostov-on-Don, 344090, Russia

    A. Mirotin

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  1. A. Mirotin
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Correspondence to A. Mirotin.

Additional information

This work was supported partly by the State Program of Scientific Research of the Republic of Belarus, project No. 20211776 and by the Ministry of Education and Science of Russia, agreement No. 075-02-2023-924.

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Mirotin, A. μ-Hankel operators on compact Abelian groups. Anal Math 49, 617–640 (2023). https://doi.org/10.1007/s10476-023-0217-3

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  • DOI: https://doi.org/10.1007/s10476-023-0217-3

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