Spectrality of the Dirac Operator with Complex-Valued Periodic Coefficients

TL;DR

This paper investigates the spectral properties of a non-self-adjoint Dirac operator with complex periodic coefficients, establishing conditions for its spectrality and analyzing spectral expansion.

Contribution

It provides new criteria for the spectrality of the Dirac operator with complex periodic potentials, expanding understanding of non-self-adjoint spectral theory.

Findings

Identifies conditions on off-diagonal elements for asymptotic spectrality

Derives criteria ensuring the spectrality of the operator

Analyzes spectral expansion under these conditions

Abstract

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 asymptotically spectral operator. Moreover, we derive a condition on Q that ensures the spectrality of this operator. Finally, we consider the spectral expansion in these cases.