The existence of complex transmission eigenvalues for spherically stratified media

Abstract

We continue our investigation of transmission eigenvalues for spherically stratified media. In particular, in the case when the index of refraction n(r) is such that , we establish conditions on n(r) to guarantee that there exists an infinite number of complex transmission eigenvalues and when , we establish very weak conditions on n(r) to guarantee the existence of complex transmission eigenvalues.

Keywords:

• Inverse scattering
• complex transmission eigenvalues
• spectral theory

AMS Subject Classifications:

• 35P05
• 35P25
• 35R30

Acknowledgements

There is a vast literature on the transmission eigenvalue problem and for a sample of this research and further references we refer reader to [16–22].

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of D. Colton was supported in part by the Air Force Office of Scientific Research [grant number FA 9550-13-1-0199].