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

2013/09/03 by T. J. Christiansen, Christiansen, T. J.
Computer Science · Mathematics · Physics and Astronomy · #35P25 #58J50 #81U05 #Advanced Mathematical Modeling in Engineering #Bounded function #Combinatorics #Cover (algebra) #Dimension (graph theory) #FOS: Mathematics #FOS: Physical sciences #Function (biology) #Lambda #Logarithm #Mathematical Physics (math-ph) #Mathematical analysis #Mathematical physics #Mathematics #Numerical methods in inverse problems #Operator (biology) #Order (exchange) #Physics #Quantum mechanics #Resonance (particle physics) #Sign (mathematics) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:35P25 #msc:58J50 #msc:81U05

paper · pdf · doi:10.48550/arxiv.1309.0754

21 pages

arxiv created 2013/09/03 · openalex publication_date 2013/09/03 · arxiv updated 2013/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 ∖ \0\. We show that for fixed sign potentials V and for nonzero integers m, the resonance counting function for the mth sheet of Λ has maximal order of growth.

Citations

• Some remarks on resonances in even-dimensional Euclidean scattering

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