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.


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
Full Text: DOI


[1] Colton, D.; Kress, R., Inverse Acoustic and Electromagnetic Scattering Theory (2012), Berlin, Germany: Springer, Berlin, Germany
[2] Cakoni, F.; Colton, D.; Gintides, D., The interior transmission eigenvalue problem, SIAM Journal on Mathematical Analysis, 42, 6, 2912-2921 (2010) · Zbl 1219.35352
[3] Leung, Y.; Colton, D., Complex transmission eigenvalues for spherically stratified media, Inverse Problems, 28, 7 (2012) · Zbl 1260.47012
[4] Colton, D.; Leung, Y., Complex eigenvalues and the inverse spectral problem for transmission eigenvalues, Inverse Problems, 29, 10 (2013) · Zbl 1305.34027
[5] Sylvester, J., Transmission eigenvalues in one dimension, Inverse Problems, 29, 10 (2013) · Zbl 1294.34079
[6] Poschel, J.; Trubowitz, E., Inverse Spectral Theory (1987), Boston, Mass, USA: Academic Press, Boston, Mass, USA · Zbl 0623.34001
[7] Colton, D.; Päivärinta, L.; Sylvester, J., The interior transmission problem, Inverse Problems and Imaging, 1, 1, 13-28 (2007) · Zbl 1130.35132
[8] Young, R. M., An Introduction to Nonharmonic Fourier Series (2001), San Diego, Calif, USA: Academic Press, San Diego, Calif, USA · Zbl 0981.42001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.