Lower bounds for resonance counting functions for Schrödinger operators with fixed sign potentials in even dimensions

  • T. J. Christiansen

    University of Missouri, Columbia, USA

Abstract

If dd is even, the resonances of the Schrödinger operator Δ+V-\Delta +V on Rd\mathbb R^d with VLcompinfty(Rd)V\in L^{infty}_{\mathrm {comp}}(\mathbb R^d) are points on Λ\Lambda, the logarithmic cover of C{0}\mathbb C \setminus \{0\}. We show that for fixed sign potentials VV and for mZ{0}m\in \mathbb Z \setminus \{0\}, the resonance counting function for the mmth sheet of Λ\Lambda has maximal order of growth.

Cite this article

T. J. Christiansen, Lower bounds for resonance counting functions for Schrödinger operators with fixed sign potentials in even dimensions. J. Spectr. Theory 5 (2015), no. 3, pp. 571–597

DOI 10.4171/JST/107