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20 papers · 1 filter
On the spectrum of the differential operators of even order with periodic matrix coefficients
O. A. Veliev
In this paper, we consider the band functions, Bloch functions and spectrum of the self-adjoint differential operator L with periodic matrix coefficients. Conditions are found for…
On the Schrodinger Operator with a Periodic PT-symmetric Matrix Potential
O. A. Veliev
In this article we obtain asymptotic formulas for the Bloch eigenvalues of the operator generated by a system of Schrodinger equations with periodic PT-symmetric complex-valued coe…
Spectral Analysis of the Schrodinger Operator with an Optical Potential
O. A. Veliev
In this paper we give a complete description of the spectral analysis of the Schrodinger operator L(V) with the optical potentil. First we consider the Bolch eigenvalues and spectr…
On the Spectrality and Spectral Expansion of the Non-self-adjoint Mathieu-Hill Operator in All Real Line
O. A. Veliev
In this paper we investigate the non-self-adjoint operator H generated in all real line by the Mathieu-Hill equation with a complex-valued potential. We find a necessary and suffic…
The Spectrum of the Hamiltonian with a PT-symmetric Periodic Optical Potential
O. A. Veliev
We give a complete description, provided with a mathematical proof, of the shape of the spectrum of the Hill operator with a PT-symmetric periodic optical potential. We prove that…
On the spectral properties of the Schrodinger operator with a periodic PT-symmetric potential
O. A. Veliev
In this paper we investigate the spectrum and spectrality of the one-dimensional Schrodinger operator with a periodic PT-symmetric complex-valued potential.