Spectral analysis of the non-selfadjoint singuler differential operator generated by a system of differential equations

This thesis consists of four chapters. In the first chapter, some basic studies about this subject have been given. In the second chapter, some basic definitions and main theorems on spectral analysis have been given. The solutions satisfying certain initial conditions of the operator L are investigated. Moreover, the resolvent of the operator L is calculated and continuous spectrum of the operator L is found. In the third chapter, the properties of the principal functions corresponding to the eigenvalues of L and the spectral singularities of L are examined. We prove that the principal functions corresponding to the eigenvalues and the spectral singularities of the operator L belong to L2(0,oo,C2) and H_ respectively. This chapter was published Journal of the "Mathematica Balkanica" onFasc.1-2, Volume 13 (1999). In the last chapter, the spectral expansion formula corresponding to the principal functions of the L operator is found and convergence of this formula is examined. Science Code : 403.03.01 Key Words : Eigenvalue, principal function, spectral singularity, spectral analysis. Page number : 63 Adviser : Assos.Prof.Cemil YILDIZ