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Scattering of plane waves and a modified Pompeiu criterion
Abstract
In this paper we prove that plane waves always scatter from bounded, strictly convex planar inhomogeneities with constant material parameters. Our approach involves the introduction of a modified Pompeiu property, whose failure corresponds to the vanishing of the Fourier transform of the indicator function of the inhomogeneity on a complexified circle not centered at the origin. We then show that such vanishing is impossible for bounded, strictly convex planar sets.
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BibTeX
@misc{hovsepyan2026scattering,
title = {{Scattering of plane waves and a modified Pompeiu criterion}},
author = {Narek Hovsepyan and Michael S. Vogelius},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30329},
eprint = {2610.30329},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30329},
}
RIS
TY - UNPB
TI - Scattering of plane waves and a modified Pompeiu criterion
AU - Narek Hovsepyan
AU - Michael S. Vogelius
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30329
UR - https://arxiv.org/abs/2610.30329
AB - In this paper we prove that plane waves always scatter from bounded, strictly convex planar inhomogeneities with constant material parameters. Our approach involves the introduction of a modified Pompeiu property, whose failure corresponds to the vanishing of the Fourier transform of the indicator function of the inhomogeneity on a complexified circle not centered at the origin. We then show that such vanishing is impossible for bounded, strictly convex planar sets.
ER -