Related papers: On the spectrum of $2\times 2$ Dirac operator with…
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…
The paper is concerned with the completeness property of root functions of the $2\times 2$ Dirac operator with summable complex-valued potential and non-regular boundary conditions. Sufficient conditions for the completeness of the root…
The paper is concerned with the completeness property of root functions of the Dirac operator with summable complexvalued potential and non-regular boundary conditions. We also obtain explicit form for the fundamental solution system of the…
In this work, we consider Dirac-type operators with a constant delay less than two-fifths of the interval and not less than one-third of the interval. For our considered Dirac-type operators, an incomplete inverse spectral problem is…
In this work, we consider Dirac-type operators with a constant delay less than half of the interval and not less than two-fifths of the interval. For our considered Dirac-type operators, two inverse spectral problems are studied.…
The paper is concerned with the basis properties of root function systems of the Dirac operator with a complex-valued summable potential. We establish a necessary condition of convergence of corresponding spectral expansions.
We initiate studying inverse spectral problems for Dirac-type functional-differential operators with constant delay. For simplicity, we restrict ourselves to the case when the delay parameter is not less than one half of the interval. For…
Spectral problem for the Dirac operator with regular but not strongly regular boundary conditions and complex-valued potential summable over a finite interval is considered. The purpose of this paper is to find conditions under which the…
In this paper, we consider spectral problem for the nth order ordinary differential operator with degenerate boundary conditions. We construct a nontrivial example of boundary value problem which has no eigenvalues.
The spectral properties of Dirac operators on $(0,1)$ with potentials that belong entrywise to $L_p(0,1)$, for some $p\in[1,\infty)$, are studied. The algorithm of reconstruction of the potential from two spectra or from one spectrum and…
We consider operators of boundary value problems for 3D- Dirac operators in unbounded domains with the uniformly regular boundary. We give effective conditions of self-adjointness of operators under consideration and a description of their…
We consider spectral problems for the Sturm-Liouville operator with arbitrary complex-valued potential q(x) and degenerate boundary conditions. We solve corresponding inverse problem, and also study the completeness property and the basis…
In this paper, we study the spectrality of the non-self-adjoint Dirac operator L(Q) with a complex-valued periodic matrix potential Q. We establish a condition on the off-diagonal elements of the matrix Q under which L(Q) is an…
In this paper, we consider a discontinuous Dirac operator depending polynomially on the spectral parameter and a finite number of transmission conditions. We get some properties of eigenvalues and eigenfunctions. Then, we investigate some…
We carry the index theory for manifolds with boundary of B\"ar and Ballmann over to first order differential operators on metric graphs. This approach results in a short proof for the index of such operators. Then the self-adjoint…
In this article, we study the spectrum of the magnetic Dirac operator, and the magnetic Dirac operator with potential over complete Riemannian manifolds. We find sufficient conditions on the potentials as well as the manifold so that the…
The two-dimensional Dirac operator describes low-energy excitations in graphene. Different choices for the boundary conditions give rise to qualitative differences in the spectrum of the resulting operator. For a family of boundary…
In this article, we provide the spectral analysis of a Dirac-type operator on $\mathbb{Z}^2$ by describing the behavior of the spectral shift function associated with a sign-definite trace-class perturbation by a multiplication operator. We…
We consider a two-dimensional massless Dirac operator coupled to a magnetic field $B$ and an electric potential $V$ growing at infinity. We find a characterization of the spectrum of the resulting operator $H$ in terms of the relation…
We consider the spectral problem generated by the Sturm-Liouville equation with an arbitrary complex-valued potential q(x) and irregular boundary conditions. We establish necessary and sufficient conditions for a set of complex numbers to…