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Article

Reconstruction of Differential Operators with Frozen Argument

by
Oles Dobosevych
† and
Rostyslav Hryniv
*,†
Faculty of Applied Sciences, Ukrainian Catholic University, 79026 Lviv, Ukraine
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Axioms 2022, 11(1), 24; https://doi.org/10.3390/axioms11010024
Submission received: 1 December 2021 / Revised: 4 January 2022 / Accepted: 6 January 2022 / Published: 9 January 2022
(This article belongs to the Special Issue Analytic Functions and Nonlinear Functional Analysis)
Versions Notes

Abstract

We study spectral properties of a wide class of differential operators with frozen arguments by putting them into a general framework of rank-one perturbation theory. In particular, we give a complete characterization of possible eigenvalues for these operators and solve the inverse spectral problem of reconstructing the perturbation from the resulting spectrum. This approach provides a unified treatment of several recent studies and gives a clear explanation and interpretation of the obtained results.
Keywords: differential operators; Sturm–Liouville-type operators; inverse problems; rank-one perturbations; frozen argument differential operators; Sturm–Liouville-type operators; inverse problems; rank-one perturbations; frozen argument

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MDPI and ACS Style

Dobosevych, O.; Hryniv, R. Reconstruction of Differential Operators with Frozen Argument. Axioms 2022, 11, 24. https://doi.org/10.3390/axioms11010024

AMA Style

Dobosevych O, Hryniv R. Reconstruction of Differential Operators with Frozen Argument. Axioms. 2022; 11(1):24. https://doi.org/10.3390/axioms11010024

Chicago/Turabian Style

Dobosevych, Oles, and Rostyslav Hryniv. 2022. "Reconstruction of Differential Operators with Frozen Argument" Axioms 11, no. 1: 24. https://doi.org/10.3390/axioms11010024

APA Style

Dobosevych, O., & Hryniv, R. (2022). Reconstruction of Differential Operators with Frozen Argument. Axioms, 11(1), 24. https://doi.org/10.3390/axioms11010024

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