An uniqueness result with some density theorems with interior transmission eigenvalues

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

MSC:

• 35P25
• 35R30
• 34B24