An uniqueness result with some density theorems with interior transmission eigenvalues |
| |
Authors: | Lung-Hui Chen |
| |
Affiliation: | 1. Department of Mathematics, National Chung Cheng University, 168 University Rd., Min-Hsiung, Chia-Yi County, 621Taiwan.lhchen@math.ccu.edu.tw |
| |
Abstract: | Given a set of transmission eigenvalues, we apply Cartwright’s theory to show the density function inversely determines the indicator function. This indicator function gives a Weyl’s type of asymptotics on the transmission eigenvalues. The inverse uniqueness problem on the refraction index is reduced to identifying a parameter of an entire function. We use a Carlson’s type of theorem to prove the uniqueness as in entire function theory. Taking advantage of the uniqueness of rod density problem, we prove an uniqueness result with interior transmission eigenvalues. |
| |
Keywords: | interior transmission eigenvalues Cartwright’s theory indicator function Carlson’s theorem Wilder’s theorem |
|
|