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Complex transmission eigenvalues in one dimension. (English) Zbl 1474.34606

Summary: We consider all of the transmission eigenvalues for one-dimensional media. We give some conditions under which complex eigenvalues exist. In the case when the index of refraction is constant, it is shown that all the transmission eigenvalues are real if and only if the index of refraction is an odd number or reciprocal of an odd number.

MSC:

34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
34A55 Inverse problems involving ordinary differential equations
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