Upper bound for the counting function of interior transmission eigenvalues

2013/08/12 by Dimassi, Mouez, Petkov, Vesselin
#35J57 #35P20 #35R30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1308.2594

Abstract

For the complex interior transmission eigenvalues (ITE) we study for small θ> 0 the counting function N(θ, r) = #\λ∈ \C: λ \rm is \rm (ITE), |λ| ≤ r, 0 ≤ arg λ≤ θ\. We obtain for fixed θ> 0 an upper bound N(θ, r) ≤ C r^n/2, r ≥ r(θ).

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