We study a one-dimensional exterior transmission eigenvalue problem with a piecewise W 2 1 {W₂¹} refractive index. We establish conditions on the refractive index under which the problem has only finitely many real transmission eigenvalues. In addition, we prove that two sets of exterior transmission eigenvalues uniquely determine the refractive index.
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Tao et al. (2026) studied this question.
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