Asymptotics of the number of the interior transmission eigenvalues

2014/03/16 by Vesselin Petkov, Petkov, Vesselin, Georgi Vodev +1
Mathematics · Physics and Astronomy · #35P15 #35P20 #35P25 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #math-ph #math.MP #math.SP #msc:35P15 #msc:35P20 #msc:35P25

paper · pdf · doi:10.48550/arxiv.1403.3949

arxiv created 2014/12/14 · arxiv updated 2014/12/16

Abstract

We prove a Weyl asymptotics N(r) = c r^d + \mathcal O_ε(r^{d - κ+ ε}), ∀ 0< ε≪ 1, for the counting function N(r) = \sharp\λ_j ∈ \mathbb C ∖ \0\: |λ_j| ≤ r²\, r>1, of the interior transmission eigenvalues (ITE), λ_j. Here 0<κ≤ 1 is such that there are no (ITE) in the region \λ∈ \mathbb C: |\rm Im λ|≥ C(| \rm Re λ|+1)^1-\fracκ2\ for some C>0.

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