Abstract In the present paper, a theorem on θ −| T; δ | k summability method of an infinite series is proved, and also by using this method, result trigonometric Fourier obtained.

A recently established general trace formula for one-dimensional Schrödinger operators is systematically studied in the context of short-range potentials, potentials which approach different spatial asymptotes sufficiently fast, and appropriate impurity (defect) interactions in one-dimensional solids. We prove the absolute summability of the trace formula and establish its connections with scat...

A recently established general trace formula for one-dimensional Schrodinger operators is systematically studied in the context of short-range potentials, potentials which approach different spatial asymptotes sufficiently fast, and appropriate impurity (defect) interactions in one-dimensional solids. We prove the absolute summability of the trace formula and establish its connections with scat...