A sub-logarithmic lower bound for resonance counting function in two-dimensional potential scattering

DOI10.1016/S0034-4877(10)00013-3zbMath1218.81101MaRDI QIDQ615182

Lung-Hui Chen

Publication date: 5 January 2011

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Schrödinger equationtrace formulaPhragmén-Lindelöf theorempotential scatteringexistence of resonanceresonance lower bound

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) (S)-matrix theory, etc. in quantum theory (81U20) Scattering theory of linear operators (47A40)

Related Items (3)

Resonant rigidity for Schrödinger operators in even dimensions ⋮ Some remarks on resonances in even-dimensional Euclidean scattering ⋮ Lower bounds for resonance counting functions for Schrödinger operators with fixed sign potentials in even dimensions

Cites Work

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• Poisson formula for resonances in even dimensions
• Sharp bounds on the number of scattering poles in even-dimensional spaces
• Lower bounds for the number of resonances in even dimensional potential scattering
• Resonant states and poles of the scattering matrix for perturbations of - \(\Delta\)
• On the absolutely continuous spectrum of multi-dimensional Schrödinger operators with slowly decaying potentials
• Sharp Bounds on the Number of Scattering Poles in the Two Dimensional Case
• Existence of Resonances in Even Dimensional Potential Scattering

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