Transmission eigenvalues and thermoacoustic tomography
Analysis of PDEs
2015-06-16 v1
Abstract
The spectrum of the interior transmission problem is related to the unique determination of the acoustic properties of a body in thermoacoustic imaging. Under a non-trapping hypothesis, we show that sparsity of the interior transmission spectrum implies a range separation condition for the thermoacoustic operator. In odd dimension greater than or equal to three, we prove that the transmission spectrum for a pair of radially symmetric non-trapping sound speeds is countable, and conclude that the ranges of the associated thermoacoustic maps have only trivial intersection.
Cite
@article{arxiv.1306.5481,
title = {Transmission eigenvalues and thermoacoustic tomography},
author = {David Finch and Kyle S. Hickmann},
journal= {arXiv preprint arXiv:1306.5481},
year = {2015}
}