On the range of the attenuated Radon transform in strictly convex sets

Sadiq, Kamran; Tamasan, Alexandru

doi:10.1090/S0002-9947-2014-06307-1

On the range of the attenuated Radon transform in strictly convex sets
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by Kamran Sadiq and Alexandru Tamasan PDF

Trans. Amer. Math. Soc. 367 (2015), 5375-5398 Request permission

Abstract:

We present new necessary and sufficient conditions for a function on $\partial \Omega \times S^1$ to be in the range of the attenuated Radon transform of a sufficiently smooth function support in the convex set $\overline \Omega \subset \mathbb {R}^2$. The approach is based on an explicit Hilbert transform associated with traces on the boundary of A-analytic functions in the sense of Bukhgeim.

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