On resonances generated by conic diffraction

2017/06/23 by Hillairet, Luc, Wunsch, Jared · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1706.07869

Abstract

We describe the resonances closest to the real axis generated by diffraction of waves among cone points on a manifold with Euclidean ends. These resonances lie asymptotically evenly spaced along a curve of the form (\Im λ)/(log |\Re λ |)= -ν; here ν=(n-1)/2 L₀ where n is the dimension and L₀ is the length of the longest geodesic connecting two cone points. Moreover there are asymptotically no resonances below this curve and above the curve (\Im λ)/(log |\Re λ |)= -Λ for a fixed Λ>ν.

Cited by

• On the convergence of the Born series for Coulomb potentials

Related

• Locating resonances on hyperbolic cones
• Diffractive Propagation on Conic Manifolds
• Resonances near the real axis for manifolds with hyperbolic trapped sets
• Low-lying resonances for infinite-area hyperbolic surfaces with long closed geodesics
• Resolvent estimates and local decay of waves on conic manifolds