# American Institute of Mathematical Sciences

May  2015, 9(2): 317-335. doi: 10.3934/ipi.2015.9.317

## On the range of the attenuated magnetic ray transform for connections and Higgs fields

 1 Trinity College, Cambridge, CB2 1TQ, United Kingdom 2 Department of Mathematics, University of Washington, Seattle, WA 98195-4350, United States

Received  November 2013 Revised  July 2014 Published  March 2015

For a two-dimensional simple magnetic system, we study the attenuated magnetic ray transform $I_{A,\Phi}$, with attenuation given by a unitary connection $A$ and a skew-Hermitian Higgs field $\Phi$. We give a description for the range of $I_{A,\Phi}$ acting on $\mathbb{C}^n$-valued tensor fields.
Citation: Gareth Ainsworth, Yernat M. Assylbekov. On the range of the attenuated magnetic ray transform for connections and Higgs fields. Inverse Problems & Imaging, 2015, 9 (2) : 317-335. doi: 10.3934/ipi.2015.9.317
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