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

T. J. Christiansen

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arXiv · 1309.0754

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

T. J. Christiansen

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Abstract

If the dimension $d$ is even, the resonances of the Schrödinger operator $-Δ+V$ on ${\mathbb R}^d$ with $V$ bounded and compactly supported are points on $Λ$, 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 $Λ$ has maximal order of growth.

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BibTeX RIS

T. J. Christiansen. 2013-09-03. Lower bounds for resonance counting functions for Schrödinger operators with fixed sign potentials in even dimensions. https://arxiv.org/abs/1309.0754

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