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On the Essential Decreasing of the Summation Order in the Abel-Lidskii Sense

Author

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  • Maksim V. Kukushkin

    (Institute of Applied Mathematics and Automation, 360000 Nalchik, Russia)

Abstract

In this paper, we consider a problem of decreasing the summation order in the Abel-Lidskii sense. The problem has a significant prehistory since 1962 created by such mathematicians as Lidskii V.B., Katsnelson V.E., Matsaev V.I., Agranovich M.S. As a main result, we will show that the summation order can be decreased from the values more than a convergence exponent, in accordance with the Lidskii V.B. results, to an arbitrary small positive number. Additionally, we construct a qualitative theory of summation in the Abel-Lidkii sense and produce a number of fundamental propositions that may represent the interest themselves.

Suggested Citation

  • Maksim V. Kukushkin, 2025. "On the Essential Decreasing of the Summation Order in the Abel-Lidskii Sense," Mathematics, MDPI, vol. 13(7), pages 1-32, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:7:p:1205-:d:1629308
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    References listed on IDEAS

    as
    1. Maksim V. Kukushkin, 2024. "Schatten Index of the Sectorial Operator via the Real Component of Its Inverse," Mathematics, MDPI, vol. 12(4), pages 1-21, February.
    2. Maksim V. Kukushkin, 2022. "Natural Lacunae Method and Schatten–Von Neumann Classes of the Convergence Exponent," Mathematics, MDPI, vol. 10(13), pages 1-27, June.
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