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THE MERCER’S THEOREM FOR PARTIAL INTEGRAL OPERATORS

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Abstract

In this paper, we study partial integral operators in Kaplansky-Hilbert module. A modular and cyclic modular spectrum of such operators is described, and a corresponding example is given. In addition, a variant of the Mercer theorem for partial integral operators with a symmetric and positive kernel has been proved.

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Funding

The first author was partially supported by the Russian Ministry of Education and Science, agreement no. 075-02-2023-914.

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Authors and Affiliations

  1. Institute for Advances Study in Mathematics, Harbin Institute of Technologies, Harbin, 150001, China

    Karimbergen Kudaybergenov

  2. North Caucasus Center for Mathematical Research, Vladikavkaz, 362027, Russia

    Karimbergen Kudaybergenov

  3. V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 9 University Street, Olmazor District, Tashkent, 100174, Uzbekistan

    Allabay Arziev & Parakhatdiin Orinbaev

  4. Department of Mathematics, Karakalpak State University, 1 Ch. Abdirov, Nukus, 230112, Uzbekistan

    Allabay Arziev

  5. K.Zhubanov ARU, 34 Moldagulova Prospect, Aktobe, 030000, Kazakhstan

    Aisulu Tangirbergen

Authors
  1. Karimbergen Kudaybergenov
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  2. Allabay Arziev
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  3. Parakhatdiin Orinbaev
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  4. Aisulu Tangirbergen
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Corresponding author

Correspondence to Allabay Arziev.

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The authors declare no competing interests.

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With deep respect, we dedicate the article to the 70th anniversary of Professor Anatoly Georgievich Kusraev.

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Kudaybergenov, K., Arziev, A., Orinbaev, P. et al. THE MERCER’S THEOREM FOR PARTIAL INTEGRAL OPERATORS. J Math Sci 271, 749–761 (2023). https://doi.org/10.1007/s10958-023-06747-w

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  • DOI: https://doi.org/10.1007/s10958-023-06747-w

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