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Regular Ordinary Differential Operators with Involution

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Abstract

The main results of the paper are related to the study of differential operators of the form

$$Ly = {y^{\left( n \right)}}\left( { - x} \right) + \sum\limits_{k = 1}^n {pk\left( x \right){y^{\left( {n - k} \right)}}\left( { - x} \right) + } \sum\limits_{k = 1}^n {{q_k}\left( x \right){y^{\left( {n - k} \right)}}} \left( x \right),\,x \in \left[ { - 1,1} \right],$$

with boundary conditions of general form concentrated at the endpoints of a closed interval. Two equivalent definitions of the regularity of boundary conditions for the operator L are given, and a theorem on the unconditional basis property with brackets of the generalized eigenfunctions of the operator L in the case of regular boundary conditions is proved.

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Funding

This work was supported by the Russian Science Foundation under grant 17-11-01215.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    V. E. Vladykina & A. A. Shkalikov

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  1. V. E. Vladykina
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  2. A. A. Shkalikov
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Correspondence to V. E. Vladykina or A. A. Shkalikov.

Additional information

Russian Text © The Author(s), 2019, published in Matematicheskie Zametki, 2019, Vol. 106, No. 5, pp. 643–659.

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Vladykina, V.E., Shkalikov, A.A. Regular Ordinary Differential Operators with Involution. Math Notes 106, 674–687 (2019). https://doi.org/10.1134/S0001434619110026

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  • DOI: https://doi.org/10.1134/S0001434619110026

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