On the Riesz basis property of the root functions in certain regular boundary value problems (Q1290793)

It is proved that the system of root functions of the boundary value problem \[ y''(x)+q(x)y=\lambda y,\quad 0<x<1, \qquad y(0)=y(1),\quad y'(0)=y'(1), \] with \(q(x)\in C^4[0,1], q(0)\neq q(1),\) forms a Riesz basis in \(L_2(0,1)\). A similar result is obtained for antiperiodic boundary conditions.