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

Abstract

If the dimension $d$ is even, the resonances of the Schrödinger operator $-\Delta +V$ on ${\mathbb{R}}^d$ with $V$ bounded and compactly supported are points on $\Lambda$, the logarithmic cover of $\mathbb{C}\setminus \{0\}$. We show that for fixed sign potentials $V$ and for nonzero integers $m$, the resonance counting function for the $m$th sheet of $\Lambda$ has maximal order of growth.

21 pages

References in corpus (2)

• Some remarks on resonances in even-dimensional Euclidean scattering
• Isoresonant complex-valued potentials and symmetries

Cited by in corpus (1)

• Lower bounds for resonance counting functions for obstacle scattering in even dimensions