Related papers: On extensions and spectral problems for fourth ord…
We consider the self-adjoint Dirac operators on a finite interval with summable matrix-valued potentials and general boundary conditions. For such operators, we study the inverse problem of reconstructing the potential and the boundary…
We consider the self-adjoint fourth-order operator with real $1$-periodic coefficients on the unit interval. The spectrum of this operator is discrete. We determine the high energy asymptotics for its eigenvalues.
Spectral components of one-dimensional Schr\"odinger operator with complex potential are investigated. An effective upper bound for the total number of eigenvalues and spectral singularities is established. For dissipative Schr\"odinger…
In this paper, we combine results on extensions of operators with recent results on the relation between the M-function and the spectrum, to examine the spectral behaviour of boundary value problems. M-functions are defined for general…
The minimal and maximal operators generated by the Bessel differential expression on the finite interval and a half-line are studied. All non-negative self-adjoint extensions of the minimal operator are described. Also we obtain a…
In this work, in the Hilbert space of vector-functions L^2 (H,(-\infty,a)\cup(b,+\infty)),a<b all normal extensions of the minimal operator generated by linear singular formally normal differential expression l(\cdot)=(d/dt+A_1,d/dt+A_2)…
In this paper we investigate the spectral expansion for the asymptotically spectral differential operators generated in all real line by ordinary differential expression of arbitrary order with periodic matrix-valued coefficients
The paper develops a theory of spectral boundary value problems from the perspective of general theory of linear operators in Hilbert spaces. An abstract form of spectral boundary value problem with generalized boundary conditions is…
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…
We give general spectral and eigenvalue perturbation bounds for a selfadjoint operator perturbed in the sense of the pseudo-Friedrichs extension. We also give several generalisations of the aforementioned extension. The spectral bounds for…
In this work, firstly the maximal sectorial linear relations are described. Later on, the discreteness of the spectrum of the linear maximal sectorial operators and asymptotical behaviour of the eigenvalues of such operators in terms of the…
In this study, we are concerned with spectral problems of second-order vector dynamic equations with two-point boundary value conditions and mixed derivatives, where the matrix-valued coefficient of the leading term may be singular, and the…
We introduce the biharmonic Steklov problem on differential forms by considering suitable boundary conditions. We characterize its smallest eigenvalue and prove elementary properties of the spectrum. We obtain various estimates for the…
We give necessary and sufficient conditions for real sequences to be the spectra of selfadjoint extensions of an entire operator whose domain may be non-dense. For this spectral characterization we use de Branges space techniques and a…
In this work we begin a theoretical and numerical investigation on the spectra of evolution operators of neutral renewal equations, with the stability of equilibria and periodic orbits in mind. We start from the simplest form of linear…
We consider self-adjoint extensions of differential operators of the type $ (-\frac{d^2}{dr^2} + \frac{l(l+1)}{r^2})^3 $ on the real semi-axis for l=1,2 with two kinds of boundary conditions: first that nullify the value of a function and…
We present a spectral analysis for matrix scaling and operator scaling. We prove that if the input matrix or operator has a spectral gap, then a natural gradient flow has linear convergence. This implies that a simple gradient descent…
Non-self-adjoint second-order ordinary differential operators on a finite interval with complex weights are studied. Properties of spectral characteristics are established and the inverse problem of recovering operators from their spectral…
The inverse problem for the differential operator pencil with complex periodic potential and discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the operator…
We study the spectral problem for the Dirac operator with degenerate boundary conditions and a complex-valued summable potential. Sufficient conditions are found under which the spectrum of the problem under consideration coincides with the…