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On Multiple Completeness of Root Functions for Ordinary Differential Polynomial Pencils with Constant Coefficients

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Abstract

In the space of square integrable functions on a finite segment, we consider a class of polynomial pencils of nth-order ordinary differential operators with constant coefficients and two-point boundary conditions (at the edges of the segment). We suppose that all roots of the characteristic equations of pencils of the said class are simple and nonzero. We find sufficient conditions for the m-multiple completeness (1 ≤ m ≤ n) of the system of root functions of pencils from the specified class in the space of square integrable functions on the said segment.

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Authors and Affiliations

  1. Saratov State University, Saratov, Russia

    V. S. Rykhlov

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  1. V. S. Rykhlov
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Correspondence to V. S. Rykhlov.

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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 63, No. 2, Proceedings of the Crimean Autumn Mathematical School-Symposium, 2017.

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Rykhlov, V.S. On Multiple Completeness of Root Functions for Ordinary Differential Polynomial Pencils with Constant Coefficients. J Math Sci 250, 683–704 (2020). https://doi.org/10.1007/s10958-020-05034-2

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  • DOI: https://doi.org/10.1007/s10958-020-05034-2

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