Upper bound for the counting function of interior transmission eigenvalues

Mouez Dimassi (1) , Vesselin Petkov (1)

1 IMB - Institut de Mathématiques de Bordeaux

For the complex interior transmission eigenvalues (ITE) we study for small $\theta > 0$ the counting function $$N(\theta, r) = #\{\lambda \in \C:\: \lambda \: {\rm is} \: {\rm (ITE)},\: |\lambda| \leq r, \: 0 \leq \arg \lambda \leq \theta\}.$$ We obtain for fixed $\theta > 0$ an upper bound $N(\theta, r) \leq C r^{n/2}, \: r \geq r(\theta).$

Domaines: Théorie spectrale [math.SP]; Equations aux dérivées partielles [math.AP]

Mouez Dimassi, Vesselin Petkov. Upper bound for the counting function of interior transmission eigenvalues. 2014. ⟨hal-00953682⟩