Remarks on modification of Helgason's support theorem (Q2709828)

The celebrated support theorem of \textit{S. Helgason} [Groups and geometric analysis. Integral geometry, invariant differential operators, and spherical functions (1984; Zbl 0543.58001)] says that the exterior problem for the Radon transform \(Rf\) on \(R^n\) has a unique solution if and only if \(f\) decays rapidly at infinity. This result was modified by \textit{J. Boman} [Contemp. Math. 140, 23-30 (1992; Zbl 0791.44003)] by assuming that \(f\) decays rapidly only in an open cone \(\Gamma\) and also decreases to some extent globally. The author proves that Boman's global decay condition has a little mistake. A correct version of this condition is presented.