collaborators

5 papers

math.SP2026

Spectrality of the Dirac Operator with Complex-Valued Periodic Coefficients

O. A. Veliev

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…

math.SP2026

Spectral Expansion for the One-Dimensional Dirac Operator with a Complex-Valued Periodic Potential

O. A. Veliev

In this paper, we construct the spectral expansion for the one dimensional non-self-adjoint Dirac operator L(Q) with a complex-valued periodic matrix potential Q. To this end, we s…

math.SP2025

A Brief Explanation of the Spectral Expansion Method for Non-Self-Adjoint Differential Operators with Periodic Coefficients

O. A. Veliev

In this paper, we briefly explain the spectral expansion problem for differential operators defined on the entire real line, generated by a differential expression with periodic, c…

math.SP2025

On the Spectrality of the Differential Operators with Periodic Coefficients

O. A. Veliev

In this paper, we establish a condition on the coefficients of differential operators generated in the space of square-integrable functions on the entire real line by an ordinary d…

math.SP2025

On Explicit Estimations for the Bloch Eigenvalues of the One-dimensional Schrödinger Operator and the Kronig-Penney Model

Cemile Nur, Oktay Veliev

In this paper, we consider the small and large eigenvalues of the one-dimensional Schrödinger operator L(q) with a periodic, real and locally integrable potential q. First we expl…