Regular Ordinary Differential Operators with Involution

The main results of the paper are related to the study of differential operators of the form $$Ly = {y( n )}( { - x} ) + ∑k = 1^n {pk( x ){y^{( {n - k} )}}( { - x} ) + } ∑k = 1^n {{q_k}( x ){y^{( {n - k} )}}} ( x ),\,x ∈ [ { - 1,1} ],$$ with boundary conditions of general form concentrated at the endpoints of a closed interval. Two equivalent definitions of the regularity of boundary conditions for the operator L are given, and a theorem on the unconditional basis property with brackets of the generalized eigenfunctions of the operator L in the case of regular boundary conditions is proved.