Discreteness Criterion for the Spectrum of the Schr\"odinger Operator on Weighted Quasimodel Manifolds

Abstract

In this paper we study the spectrum of the Schrödinger operator on the weighted quasimodel manifolds. We obtain the discreteness criterion for this problem with some restrictions on the potential and geometry of the manifold.

Regular Potential Approximation for $\delta$-Perturbation Supported by Curve of the Laplace-Beltrami Operator on the Sphere

“…Riemannian manifold) [6][7][8]. The spectra of the Hamiltonians for spaces of different geometries are investigated in [3,13,26]. The theory of self-adjoint operators perturbed by potential supported by a set of zero measure (point, curve, etc.)…”