A regularized trace formula for second order differential operator equations

Abstract

In this paper, we deal with abstract Sturm-Liouville problems when the potential of the differential equation is an operator function in a Hilbert space $H$. We generalize trace formula obtained by [7], [9] for the classic regular Sturm-Liouville problems. We investigate the spectrum and obtained a regularized trace formula for the Sturm-Liouville operator with an operator coefficient.