143
Views
15
CrossRef citations to date
0
Altmetric
Articles

The existence of complex transmission eigenvalues for spherically stratified media

&
Pages 39-47 | Received 27 Jan 2016, Accepted 05 Jul 2016, Published online: 27 Jul 2016

References

  • Cakoni F, Colton D. A qualitative approach to inverse scattering theory. New York (NY): Springer-Verlag; 2014.
  • Guo Y, Monk P, Colton D. Toward a time domain approach to the linear sampling method. Inverse Prob. 2013;29:095016.
  • Guo Y, Monk P, Colton D. The linear sampling method for sparse small aperture data. Applicable Anal. 2016;95:1599–1615.
  • Colton D, Leung YJ, Meng S. Distribution of complex transmission eigenvalues for spherically stratified media. Inverse Prob. 2015;31:104008.
  • Leung Y, Colton D. Complex transmission eigenvalues for spherically stratified media. Inverse Prob. 2012;28:075005.
  • Kirsch A. An introduction to the mathematical theory of inverse problems. 2nd ed. Berlin: Springer-Verlag; 2011.
  • Levitan BM. Generalized translation operators and some of their applications. New York (NY): D. Davey and Company; 1964.
  • Colton D, Monk P. The inverse scattering problem for time-harmonic acoustic waves in an inhomogeneous medium. Quart. J. Mech. Appl. Math. 1988;41:97–125.
  • McLaughlin J, Polyakov P. On the uniqueness of a spherically symmetric speed of sound from transmission eigenvalues. J. Differ. Equs. 1994;107:351–382.
  • Boas R. Entire functions. New York (NY): Academic Press; 1954.
  • Koosis P. The logarithmic integral. Vol. 1. Cambridge: Cambridge University; 1998.
  • Rundell W, Sacks P. Reconstruction techniques for classical inverse Sturm--Liouville problems. Math Comput. 1992;58:161–183.
  • Erdélyi A, editor. Bateman manuscript project, Table of integral transforms. Vol. 1. New York (NY): McGraw Hill; 1954.
  • Colton D, Leung YJ. Complex eigenvalues and the inverse spectral problem for transmission eigenvalues. Inverse Prob. 2013;29:104008.
  • Colton D, Leung YJ. On a transmission eigenvalue problem for a spherically stratified coated dielectric. Inverse Prob. Imaging. 2016;10:369–377.
  • Aktosun T, Gintides D, Papanicolaou VG. The uniqueness in the inverse problem for transmission eigenvalues for the spherically-symmetric variable-speed equation. Inverse Prob. 2011;27:115004.
  • Aktosun T, Papanicolaou VG. Reconstruction of the wave speed from transmission eigenvalues for the spherically symmetric variable-speed wave equation. Inverse Prob. 2013;29:065007, 19 p.
  • Cakoni F, Colton D, Gintides D. The interior transmission eigenvalue problem. SIAM J. Math Anal. 2010;42:2912–2921.
  • Colton D, Cakoni F, Haddar H. The interior transmission eigenvalue problem for absorbing media. Inverse Prob. 2012;28:045005.
  • Cakoni F, Haddar H, editors. Special issue on transmission eigenvalues. Inverse Prob. 2013;29:100201.
  • Colton D, Monk P. The inverse scattering problem for time-harmonic acoustic waves in an inhomogeneous medium. Quart. J. Mech. Appl. Math. 1988;41:97–125.
  • Colton D, Päivärinta L, Sylvester J. The interior transmission problem. Inverse Prob. Imaging. 2007;1:13–28.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.