Sufficient Condition for Convergence of Lagrange–Sturm–Liouville Processes in Terms of One-Sided Modulus of Continuity

Resumo

A sufficient condition for the uniform convergence in the interval (0, π) of interpolation processes based on the eigenfunctions of a regular Sturm–Liouville problem with a continuous bounded variation potential is obtained. The condition is formulated in terms of a one-sided modulus of continuity of a function.