Riesz bases formed by root functions of a functional-differential equation with a reflection operator

We find conditions under which the system of root functions of the operator

$$L_y = l[y] = ay'(x) + y'(1 - x) + p_1 (x)y(x) + p_2 (x)y(1 - x),x in [0,1],U_1 (y) = intlimits_0^1 {y(t)dsigma (t) = 0,} $$

is a Riesz basis in L ₂[0, 1].