# The interior transmission eigenvalue problem

Fioralba Cakoni, David Colton, Drossos Gintides

Research output: Contribution to journalArticle

49 Citations (Scopus)

### Abstract

We consider the inverse problem of determining the spherically symmetric index of refraction n(r) from a knowledge of the corresponding transmission eigenvalues (which can be determined from field pattern of the scattered wave). We also show that for constant index of refraction n(r) = n, the smallest transmission eigenvalue suffices to determine n, complex eigenvalues exist for n sufficiently small and, for homogeneous media of general shape, determine a region in the complex plane where complex eigenvalues must lie.

Original language English (US) 2912-2921 10 SIAM Journal on Mathematical Analysis 42 6 https://doi.org/10.1137/100793542 Published - Dec 1 2010

### Fingerprint

Transmission Problem
Refraction
Eigenvalue Problem
Interior
Eigenvalue
Inverse problems
Argand diagram
Inverse Problem

### All Science Journal Classification (ASJC) codes

• Analysis
• Computational Mathematics
• Applied Mathematics

### Keywords

• Inhomogeneous medium
• Interior transmission problem
• Inverse scattering
• Transmission eigenvalues

### Cite this

Cakoni, Fioralba ; Colton, David ; Gintides, Drossos. / The interior transmission eigenvalue problem. In: SIAM Journal on Mathematical Analysis. 2010 ; Vol. 42, No. 6. pp. 2912-2921.
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The interior transmission eigenvalue problem. / Cakoni, Fioralba; Colton, David; Gintides, Drossos.

In: SIAM Journal on Mathematical Analysis, Vol. 42, No. 6, 01.12.2010, p. 2912-2921.

Research output: Contribution to journalArticle

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AU - Cakoni, Fioralba

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AU - Gintides, Drossos

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