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We study an inverse spectral problem for arbitrary order ordinary differential equations on compact star-type graphs when differential equations have regular singularities at boundary vertices. As the main spectral characteristics we…

Spectral Theory · Mathematics 2014-10-09 Vjacheslav Yurko

We review basic ideas and basic examples of the theory of the inverse spectral problems.

Mathematical Physics · Physics 2007-05-23 I. M. Krichever , S. P. Novikov

We consider a first order operator with a periodic 3x3 matrix potential on the real line. This operator appears in the problem of the periodic vector NLS equation. The spectrum of the operator covers the real line, it is union of the…

Mathematical Physics · Physics 2024-12-09 Evgeny Korotyaev

The authors study the spectral theory of self-adjoint operators that are subject to certain types of perturbations. An iterative introduction of infinitely many randomly coupled rank-one perturbations is one of our settings. Spectral…

Spectral Theory · Mathematics 2019-02-08 Dale Frymark , Constanze Liaw

We study the non-selfadjoint Dirac system on a finite interval having non-integrable regular singularities in interior points with additional matching conditions at these points. Properties of spectral characteristics are established, and…

Spectral Theory · Mathematics 2015-02-02 Oleg Gorbunov , Vjacheslav Yurko

Second order nonlinear eigenvalue problems are considered for which the spectrum is an interval. The boundary conditions are of Robin and Dirichlet type. The shape and the number of solutions are discussed by means of a phase plane…

Dynamical Systems · Mathematics 2025-04-11 Catherine Bandle , Simon Stingelin , Alfred Wagner

We define the concept of instability index of an isolated eigenvalue of a non-self-adjoint operator, and prove some of its general properties. We also describe a stable procedure for computing this index for Schroedinger operators in one…

Spectral Theory · Mathematics 2025-10-20 A. Aslanyan , E. B. Davies

We consider semi-infinite Jacobi matrices with discrete spectrum. We prove that the Jacobi operator can be uniquely recovered from one spectrum and subsets of another spectrum and norming constants corresponding to the first spectrum. We…

Spectral Theory · Mathematics 2023-10-25 Burak Hatinoğlu

In the paper the conditions are obtained providing existence and uniqueness of the regular solution of the boundary problem for class of the second order homogeneous operator-differential equation with singular coefficients. High term of…

Functional Analysis · Mathematics 2009-10-06 Rustamova Lamiya Aladdin

We suggest a new formulation of the inverse spectral problem for second-order functional-differential operators on star-shaped graphs with global delay. The latter means that the delay, being measured in the direction to a specific boundary…

Spectral Theory · Mathematics 2023-04-28 Sergey Buterin

We consider the Schrodinger operator in n-dimensional rectangular domains with either Dirichlet or Neumann boundary conditions on the faces and study the constraints on the potential imposed by fixing the spectrum of the operator.We study…

Analysis of PDEs · Mathematics 2015-07-21 Gregory Eskin , James Ralston

We consider the inverse dynamic problem for the wave equation with a potential on an interval $(0,2\pi)$ with periodic boundary conditions. We use a boundary triplet to set up the initial-boundary value problem. As an inverse data we use a…

Analysis of PDEs · Mathematics 2025-05-27 A. S. Mikhaylov , V. S. Mikhaylov

We study an inverse spectral problem for singular AKNS operators based on spectral data associated with two distinct values of the effective angular momentum parameter $\kappa\,$. Our main focus is the local inverse problem near the zero…

Analysis of PDEs · Mathematics 2026-03-24 Damien Gobin , Benoît Grébert , Bernard Helffer , François Nicoleau

Negative-index metamaterials possess a negative refractive index and thus present an interesting substance for designing uncommon optical effects such as invisibility cloaking. This paper deals with operators encountered in an…

Mathematical Physics · Physics 2024-12-16 Tomáš Faikl

Explicit inversion formulas for a subclass of integral operators with $D$-difference kernels on a finite interval are obtained. A case of the positive operators is treated in greater detail. An application to the inverse problem to recover…

Classical Analysis and ODEs · Mathematics 2009-11-20 A. L. Sakhnovich , A. A. Karelin , J. Seck-Tuoh-Mora , G. Perez-Lechuga , M. Gonzalez-Hernandez

In this paper we consider the Bloch eigenvalues and spectrum of the non-self-adjoint differential operator L generated by the differential expression of odd order n with the periodic PT-symmetric coefficients, where n>1. We study the…

Spectral Theory · Mathematics 2023-07-27 O. A. Veliev

In this paper, a diffusion operator including conformable fractional derivatives of order {\alpha} ({\alpha} in (0,1)) is considered. The asymptotics of the eigenvalues, eigenfunctions and nodal points of the operator are obtained.…

Spectral Theory · Mathematics 2023-01-03 Yaşar Çakmak

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

We consider initial value problems for differential-algebraic equations in a possibly infinite-dimensional Hilbert space. Assuming a growth condition for the associated operator pencil, we prove existence and uniqueness of solutions for…

Classical Analysis and ODEs · Mathematics 2017-11-15 Sascha Trostorff , Marcus Waurick

In this study, the theorem on necessary and sufficient conditions for the solvability of inverse problem for Sturm-Liouville operator with discontinuous coefficient is proved and the algorithm of reconstruction of potential from spectral…

Spectral Theory · Mathematics 2016-04-21 Döne Karahan , Khanlar. R. Mamedov