Uniqueness of the solution to inverse scattering problem with backscattering data

Key words: inverse scattering, non-overdetermined data, backscattering

Comparison of the singular numbers of correct restrictions of elliptic differential operators

The paper is dedicated to finding the asymptotics of singular numbers of a correct restriction of a uniformly elliptic differential operator of order 2l defined on a bounded domain in ℝn with sufficiently smooth boundary, which is in general a nonselfadjoint operator. Conditions are established on a correct restriction, ensuring that its singular numbers sk are of order k2l/n as k→∞. As an application of this result certain estimates are obtained for the deviation upon domain perturbation of singular numbers of such correct restrictions. © 2014 V. I. Burenkov and M. Otelbaev

Comparison of the singular numbers of correct restrictions of elliptic differential operators

The paper is dedicated to finding the asymptotics of singular numbers of a correct restriction of a uniformly elliptic differential operator of order 2l defined on a bounded domain in ℝn with sufficiently smooth boundary, which is in general a nonselfadjoint operator. Conditions are established on a correct restriction, ensuring that its singular numbers sk are of order k2l/n as k→∞. As an application of this result certain estimates are obtained for the deviation upon domain perturbation of singular numbers of such correct restrictions. © 2014 V. I. Burenkov and M. Otelbaev

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

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.