The discreteness of the spectrum of the Schrödinger operator equation and some properties of the s-numbers of the inverse Schrödinger operator

Abstract

In this article, we investigate the discreteness and some other properties of the spectrum for the Schrödinger operator L defined by the formula LY=-d 2 y/dx 2 +A(A+I)/x 2 y+Q(x)y on the space L 2 (H, [0, ?)), where H is a Hilbert space. For the first time, an estimate is obtained for sum of the s-numbers of the inverse Schrödinger operator. The obtained results were applied to the Laplace's equation in an angular region.