Spectral Analysis of Differential Operator with Involution

The paper deals with the differential operator $L$ with involution, defined by a differential expression $l(y)=y'(x) - q(x)y(\omega-x)$ where $q\in L_2[0,\omega]$ and boundary conditions $y(0)=y(\omega).$ The method of similar operators is used to analyze the spectral properties of the operator. The asymptotic of spectrum and the estimations for equiconvergence of spectral decomposition are obtained.