On the Spectral Expansion Formula for a Class of Dirac Operators

O. Akcaya,* and Kh. R. Mamedovb

On the Spectral Expansion Formula for a Class of Dirac Operators

Authors :

O. Akcay^a,* and Kh. R. Mamedov^b

Author Address :

^a,bDepartment of Mathematics, Mersin University, 33343, Mersin, Turkey.

*Corresponding author.

Abstract :

This paper deals with a problem for the canonical Dirac differential equations system with piecewise continuous coefficient and spectral parameter dependent in boundary conditions. The resolvent operator is constructed. The completeness theorem for eigenvector functions is proved. The spectral expansion formula with respect to eigenvector functions is obtained and Parseval equality is given.

Keywords :

Dirac operator, completeness theorem, expansion formula.

DOI :

Article Info :

Received : March 17, 2016; Accepted : April 14, 2016.