Estimate for the difference of the first derivatives of partial sums arising by non-selfadjoint Sturm-Liouville operators

Abstract

In this paper we prove an exact estimate for the difference of the first derivatives of the partial sums arising by non-selfadjoint Sturm-Liouville operators. Our result extends to that of [3] for the case when the eigenvalues may be arbitrary complex numbers. The present proof is based on an efficient method due to V. A. Il'in [6], [7].