Sharp upper bounds on the number of the scattering poles

2004/12/30 by Plamen Stefanov, Stefanov, Plamen
Mathematics · Physics and Astronomy · #35P25 #Analysis of PDEs (math.AP) #Combinatorics #Computer science #Constant (computer programming) #FOS: Mathematics #FOS: Physical sciences #Function (biology) #Geometric Analysis and Curvature Flows #Laplace operator #Mathematical Physics (math-ph) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Point processes and geometric inequalities #Quantum mechanics #Resonance (particle physics) #Scattering #Spectral Theory in Mathematical Physics #Type (biology) #Upper and lower bounds #math-ph #math.AP #math.MP #msc:35P25

paper · pdf · doi:10.48550/arxiv.math/0412536

arxiv created 2004/12/30 · openalex publication_date 2004/12/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

For various compactly supported perturbations of the Laplacian in odd dimensions n, we prove a sharp upper bound of the resonance counting function N(r) of the type N(r) ≤ A_n rⁿ(1+o(1)) with an explicit constant A_n. In a few special cases, we show that this estimate turns into an asymptotic.

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