Upper bound for the counting function of interior transmission eigenvalues

Abstract

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

References in corpus (5)

• Spectral analysis on interior transmission eigenvalues
• Applications of elliptic operator theory to the isotropic interior transmission eigenvalue problem
• Remarks on interior transmission eigenvalues, Weyl formula and branching billiards
• Bounds on positive interior transmission eigenvalues
• Transmission Eigenvalues in One Dimension

Cited by in corpus (1)

• Transmission eigenvalue-free regions