Abstract
Functional-differential operators with involution \(\nu(x)=1-x\), related to integral operators whose kernels can have points of discontinuity on the lines \(t=x\) and \(t=1-x\) and to Dirac and Sturm–Liouville operators, are used in the study of these operators and various applications. This paper provides a survey on the spectral properties of such operators with involution and their applications in problems on geometric graphs, in the study of Dirac systems, and in the justification of the Fourier method in mixed problems for partial differential equations.
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Funding
The research is fulfilled under financial support of the Russian Science Foundation (project no. 19-11-00197, carried out at the Voronezh State University).
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Communicated by V. G. Zvyagin.
Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 5, pp. 89–97.
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Burlutskaya, M.S. Some Properties of Functional-Differential Operators with Involution \(\nu(x)=1-x\) and Their Applications. Russ Math. 65, 69–76 (2021). https://doi.org/10.3103/S1066369X21050108
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DOI: https://doi.org/10.3103/S1066369X21050108