Fractal upper bounds on the density of semiclassical resonances

2005/06/15 by J. Sjoestrand, Sjoestrand, J., M. Zworski +1 · 1 citation
Mathematics · #35B34 #35P20 #35S05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP) #math.AP #math.SP #msc:35B34 #msc:35P20 #msc:35S05

paper · pdf · doi:10.48550/arxiv.math/0506307

arxiv created 2005/06/15 · arxiv updated 2009/12/01

Abstract

For semiclassical problems we establish upper bounds on the number of resonances in boxes of size h along the real axis, in terms of the dimension of the set of trapped trajectories. The proof uses second microlocalization.

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