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The inverse spectral problem is studied for the Sturm-Liouville operator with a complex-valued potential and arbitrary entire functions in one of the boundary conditions. We obtain necessary and sufficient conditions for uniqueness, and…

Spectral Theory · Mathematics 2021-09-01 Natalia Bondarenko

The inverse spectral problem is solved for the class of Sturm-Liouville operators with singular real-valued potentials from the space $W^{-1}_2(0,1)$. The potential is recovered via the eigenvalues and the corresponding norming constants.…

Spectral Theory · Mathematics 2007-05-23 R. O. Hryniv , Ya. V. Mykytyuk

This paper deals with the inverse spectral problem for a non-self-adjoint Sturm-Liouville operator with discontinuous conditions inside the interval. We obtain that if the potential $q$ is known a priori on a subinterval $ \left[ b,\pi…

Spectral Theory · Mathematics 2019-01-03 Jun Yan , Guoliang Shi

Necessary and sufficient conditions are presented for a measure to be the spectral measure of a finite range or exponentially decaying perturbation of a periodic Jacobi operator. As a corollary we can fully solve the inverse resonance…

Classical Analysis and ODEs · Mathematics 2014-09-23 Rostyslav Kozhan

In this paper, the uniform stability of the inverse spectral problem is proved for the matrix Sturm-Liouville operator on a finite interval. Namely, we describe the sets of spectral data, on which the inverse spectral mapping is bounded…

Spectral Theory · Mathematics 2026-02-17 Natalia P. Bondarenko

Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…

Dynamical Systems · Mathematics 2025-08-25 Quinlan Leishman , Benjamin Webb

Inverse spectral problems for Sturm-Liouville operators with nonlocal boundary conditions are studied. As the main spectral characteristics we introduce the so-called Weyl-type function and two spectra, which are generalizations of the…

Spectral Theory · Mathematics 2014-10-09 Vjacheslav Yurko , Chuan-Fu Yang

Stability of linear systems with uncertain bounded time-varying delays is studied under assumption that the nominal delay values are not equal to zero. An input-output approach to stability of such systems is known to be based on the bound…

Optimization and Control · Mathematics 2007-05-23 Eugenii Shustin , Emilia Fridman

The main goal of this paper is to propose an approach to inverse spectral problems for functional-differential operators (FDO) with involution. For definiteness, we focus on the second-order FDO with involution-reflection. Our approach is…

Spectral Theory · Mathematics 2021-07-27 Natalia P. Bondarenko

We suggest a new concept of functional-differential operators with constant delay on geometrical graphs that involves {\it global} delay parameter. Differential operators on graphs model various processes in many areas of science and…

Spectral Theory · Mathematics 2022-11-01 Sergey Buterin

We solve the inverse problems to recover Dirac systems on an interval or semiaxis from their spectral functions (matrix valued functions) for the case of locally square-integrable potentials. Direct problems in terms of spectral functions…

Spectral Theory · Mathematics 2026-04-29 Alexander Sakhnovich

Given a one-dimensional weighted Dirac operator we can define a spectral measure by virtue of singular Weyl-Titchmarsh-Kodaira theory. Using the theory of de Branges spaces we show that the spectral measure uniquely determines the Dirac…

Spectral Theory · Mathematics 2015-06-26 Jonathan Eckhardt , Aleksey Kostenko , Gerald Teschl

In this paper, we consider the recovery of third-order differential operators from two spectra, as well as fourth-order or fifth-order differential operators from three spectra, where these differential operators are endowed with…

Spectral Theory · Mathematics 2024-02-29 Ai-Wei Guan , Chuan-Fu Yang , Natalia P. Bondarenko

The paper deals with nonlocal differential operators possessing a term with frozen (fixed) argument appearing, in particular, in modelling various physical systems with feedback. The presence of a feedback means that the external affect on…

Spectral Theory · Mathematics 2021-03-16 Sergey Buterin , Yi-Teng Hu

In this paper, we consider a class of matrix functions, which contains regularization matrices of Mirzoev and Shkalikov for differential operators with distribution coefficients of order $n \ge 2$. We show that every matrix function of this…

Spectral Theory · Mathematics 2023-08-10 Natalia P. Bondarenko

We consider massless Dirac operators on the real line with compactly supported potentials. We solve two inverse problems (including characterization): in terms of zeros of reflection coefficient and in terms of poles of reflection…

Mathematical Physics · Physics 2020-09-16 Evgeny Korotyaev , Dmitrii Mokeev

Let $\Omega =\omega\times\mathbb R$ where $\omega\subset \mathbb R^2$ be a bounded domain, and $V : \Omega \to\mathbb R$ a bounded potential which is $2\pi$-periodic in the variable $x_{3}\in \mathbb R$. We study the inverse problem…

Analysis of PDEs · Mathematics 2016-02-01 Otared Kavian , Yavar Kian , Eric Soccorsi

We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary…

Spectral Theory · Mathematics 2013-03-22 David Andrew Smith , Beatrice Pelloni

The matrix Sturm-Liouville operator on a finite interval with singular potential of class $W_2^{-1}$ and the general self-adjoint boundary conditions is studied. This operator generalizes the Sturm-Liouville operators on geometrical graphs.…

Spectral Theory · Mathematics 2020-07-16 Natalia P. Bondarenko

This paper deals with the Sturm-Liouville problem with singular potential of the Sobolev space $W_2^{-1}$ and polynomials of the spectral parameter in a boundary condition. We prove the uniform boundedness and the uniform stability for the…

Spectral Theory · Mathematics 2025-04-08 N. P. Bondarenko , E. E. Chitorkin