A sharp lower bound for a resonance-counting function in even dimensions

2015/10/16 by T. J. Christiansen, Christiansen, T. J.
Mathematics · Physics and Astronomy · #35P25 #58J50 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #math-ph #math.MP #math.SP #msc:35P25 #msc:58J50

paper · pdf · doi:10.48550/arxiv.1510.04952

21 pages

arxiv created 2015/10/16 · arxiv updated 2015/10/19

Abstract

This paper proves sharp lower bounds on a resonance counting function for obstacle scattering in even-dimensional Euclidean space without a need for trapping assumptions. Similar lower bounds are proved for some other compactly supported perturbations of the Laplacian on even-dimensional Euclidean space, for example, for the Laplacian for certain metric perturbations. The proof uses a Poisson formula for resonances, complementary to one proved by Zworski in even dimensions.

Related

• Counting the Resonances in High and Even Dimensional Obstacle Scattering
• Lower bounds for resonance counting functions for obstacle scattering in even dimensions
• Sharp upper bounds on resonances for perturbations of hyperbolic space
• Sharp upper bounds on the number of the scattering poles
• Poisson Formula for Resonances in Even Dimensions