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) + ₊ = ₁ⁿ pk (x) {y^{ ({n - k) }} (- x) + } ₊ = ₁ⁿ {qₖ (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.