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- W4386875666 abstract "We consider the Calder'on problem for systems with unknown zeroth and first order terms, and improve on previously known results. More precisely, let $(M, g)$ be a compact Riemannian manifold with boundary, let $A$ be a connection matrix on $E = M times mathbb{C}^r$ and let $Q$ be a matrix potential. Let $Lambda_{A, Q}$ be the Dirichlet-to-Neumann map of the associated connection Laplacian with potential $mathcal{L}_{A, Q}$. Under the assumption that $(M, g)$ is isometrically contained in the interior of $(mathbb{R}^2 times M_0, c(e oplus g_0))$, where $(M_0, g_0)$ is an arbitrary compact Riemannian manifold with boundary, $e$ is the Euclidean metric on $mathbb{R}^2$, and $c > 0$, we show that $Lambda_{A, Q}$ uniquely determines $(A, Q)$ up to natural gauge invariances. Moreover, we introduce a new complex ray transform and a new complex parallel transport problem, and study their fundamental properties and relations to the Calder'on problem." @default.
- W4386875666 created "2023-09-20" @default.
- W4386875666 creator A5005842774 @default.
- W4386875666 date "2023-09-17" @default.
- W4386875666 modified "2023-09-27" @default.
- W4386875666 title "Calder'on problem for systems via complex ray transform" @default.
- W4386875666 doi "https://doi.org/10.48550/arxiv.2309.09348" @default.
- W4386875666 hasPublicationYear "2023" @default.
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