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Spectral decomposition of self-adjoint cyclically compact operators and partial integral equations

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Abstract

We prove a spectral decomposition theorem for self-adjoint cyclically compact operators on Hilbert–Kaplansky module over a ring of bounded measurable functions. We apply this result to partial integral equations on the space with mixed norm of measurable functions. We give a condition of solvability of partial integral equations with self-adjoint kernel.

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Authors and Affiliations

  1. Department of Mathematics, Karakalpak State University, 230113, Nukus, Uzbekistan

    K. Kudaybergenov

  2. Department of Computational & Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, P.O. Box 141, 25710, Kuantan, Pahang, Malaysia

    F. Mukhamedov

Authors
  1. K. Kudaybergenov
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  2. F. Mukhamedov
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Correspondence to F. Mukhamedov.

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Kudaybergenov, K., Mukhamedov, F. Spectral decomposition of self-adjoint cyclically compact operators and partial integral equations. Acta Math. Hungar. 149, 297–305 (2016). https://doi.org/10.1007/s10474-016-0619-9

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  • DOI: https://doi.org/10.1007/s10474-016-0619-9

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