Regular Ordinary Differential Operators with Involution

The main results of the paper are related to the study of differential operators of the form
$$ Ly = y^{(n)}(-x) + \sum_{k=1}^n p_k(x) y^{(n-k)}(-x) + \sum_{k=1}^n q_k(x) y^{(n-k)}(x),\qquad \ x\in [-1,1], $$
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.