Universal inequalities and bounds for weighted eigenvalues of the Schrödinger operator on the Heisenberg group.

For a bounded domain Ω in the Heisenberg group ℍn, we investigate the Dirichlet weighted eigenvalue problem of the Schrödinger operator Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed., where Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. is the Kohn Laplacian and V is a nonnegative potential. We establish a Yang-type inequality for eigenvalues of this problem. It contains the sharpest result for Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. in [17] of Soufi, Harrel II and Ilias. Some estimates for upper bounds of higher order eigenvalues and the gaps of any two consecutive eigenvalues are also derived. Our results are related to some previous results for the Laplacian Δ and the Schrödinger operator -Δ + V on a domain in ℝn and other manifolds. [ABSTRACT FROM AUTHOR]