A criterion of convergence of Lagrange–Sturm–Liouville processes in terms of one-sided modulus of variation

We obtain a criterion of uniform convergence inside the interval $(0, \pi)$ of interpolation processes constructed from eigenfunctions of the regular Sturm–Liouville problem with a continuous potential of bounded variation. The condition of the characteristic is formulated in terms of a one-sided modulus of variations of the function.