Sharp Bounds on the Number of Scattering Poles in the Two Dimensional Case

DOI10.1002/mana.19941700120zbMath0829.35091OpenAlexW2013275518MaRDI QIDQ4321264

Georgi Vodev

Publication date: 2 February 1995

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.19941700120

zbMATH Keywords

resonancesmeromorphic continuationscattering poles

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Diffraction, scattering (78A45) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (13)

Sharp upper bounds on the number of the scattering poles ⋮ Resonant rigidity for Schrödinger operators in even dimensions ⋮ A sub-logarithmic lower bound for resonance counting function in two-dimensional potential scattering ⋮ A sharp lower bound for a resonance-counting function in even dimensions ⋮ Singularities of the scattering kernel for trapping obstacles ⋮ Lower bounds for the number of resonances in even dimensional potential scattering ⋮ A quantitative Vainberg method for black box scattering ⋮ Mathematical study of scattering resonances ⋮ Schrödinger operators with complex-valued potentials and no resonances ⋮ 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 ⋮ Distribution of Resonances in Scattering by Thin Barriers ⋮ Existence of Resonances in Even Dimensional Potential Scattering

Cites Work

• Polynomial bound on the number of scattering poles
• Sharp polynomial bounds on the number of scattering poles
• Sharp polynomial bounds on the number of scattering poles for metric perturbations of the Laplacian in \(\mathbb{R}{}^ n\)
• Sharp bounds on the number of scattering poles for perturbations of the Laplacian
• Sharp bounds on the number of scattering poles in even-dimensional spaces
• Sharp polynomial bounds on the number of scattering poles of radial potentials
• Lower bounds on the number of scattering poles
• A polynomial bound on the number of the scattering poles for a potential in even dimensional spaces IRⁿ
• Complex Scaling and the Distribution of Scattering Poles

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