Theorem of completeness for a Dirac-type operator with generalized $\lambda$-depending boundary conditions

TL;DR

This paper proves a completeness theorem for a Dirac-type operator with generalized lambda-dependent boundary conditions and establishes conditions under which the root functions form a Riesz basis.

Contribution

It introduces a completeness theorem for a system of integro-differential equations with lambda-dependent boundary conditions and provides criteria for the root functions to form a Riesz basis.

Findings

Proved a completeness theorem for the operator

Established sufficient conditions for root functions to form a Riesz basis

Analyzed lambda-dependent boundary conditions

Abstract

A completeness theorem is proved involving a system of integro-differential equations with some $\lambda$-depending boundary conditions. Also some sufficient conditions for the root functions to form a Riesz basis are established.