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Asymptotics of the number of the interior transmission eigenvalues
Language
en
Article de revue
This item was published in
Journal of Spectral Theory. 2017-03-25, vol. 7, n° 1, p. 1-31
European Mathematical Society
English Abstract
We prove Weyl asymptotics $N(r) = c r^d + {\mathcal O}_{\epsilon}(r^{d - \kappa + \epsilon})$, $\forall\, 0< \epsilon \ll 1$, for the counting function $N(r) = \sharp\{\lambda_j \in \C \setminus \{0\}:\: |\lambda_j| \leq ...Read more >
We prove Weyl asymptotics $N(r) = c r^d + {\mathcal O}_{\epsilon}(r^{d - \kappa + \epsilon})$, $\forall\, 0< \epsilon \ll 1$, for the counting function $N(r) = \sharp\{\lambda_j \in \C \setminus \{0\}:\: |\lambda_j| \leq r^2\}$, $r>1$, of the interior transmission eigenvalues (ITE), $\lambda_j$. Here $0<\kappa\le 1$ is such that there are no (ITE) in the region $\{\lambda\in \C:\: |{\rm Im}\,\lambda|\ge C(| {\rm Re}\,\lambda|+1)^{1-\frac{\kappa}{2}}\}$ for some $C>0$.Read less <
English Keywords
Interior transmission eigenvalues
Weyl formula with remainder
eigenvalue-free regions
ANR Project
Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020
Origin
Hal imported