On a necessary condition of convergence of spectral expansions corresponding to the Dirac operators

TL;DR

This paper investigates the basis properties of root functions of Dirac operators with complex potentials, establishing a necessary condition for the convergence of their spectral expansions.

Contribution

It introduces a new necessary condition for the convergence of spectral expansions related to Dirac operators with complex potentials.

Findings

Identifies a necessary condition for spectral expansion convergence.

Enhances understanding of basis properties of Dirac operator root functions.

Provides theoretical insights into spectral analysis of complex-valued potentials.

Abstract

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.