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Comment to “Remarks on modification of Helgason’s support theorem. II” by T. Takiguchi. (English) Zbl 1161.44300

Summary: We slightly extend a uniqueness theorem for generalized Radon transforms \(f\mapsto Rf\) proved by J. Boman [Contemp. Math. 140, 23–30 (1992; Zbl 0791.44003)], by giving sharp decay conditions on the function \(f\) at infinity.
[Concerns also T. Takiguchi, Proc. Japan Acad., Ser. A 77, No. 6, 87–91,loose errata (2001; Zbl 0991.44001).]

MSC:

44A12 Radon transform
30E10 Approximation in the complex plane
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References:

[1] Boman, J.: Helgason’s support theorem for Radon transforms - a new proof and a generalization. Lecture Notes in Math., no.,1497, Springer, Berlin, pp. 1-5 (1989). · Zbl 0772.44003 · doi:10.1007/BFb0084503
[2] Boman, J.: Holmgren’s uniqueness theorem and support theorems for real analytic Radon transforms. Contemp. Math., 140 , 23-30 (1992). · Zbl 0791.44003
[3] Helgason, S.: The Radon transform. Birkhäuser (1980). · Zbl 0453.43011
[4] Takiguchi, T.: Remarks on modification of Helgason’s support theorem. J. Inv. Ill-posed Problems, 8 , 573-579 (2000). · Zbl 0979.44001 · doi:10.1515/jiip.2000.8.5.573
[5] Takiguchi, T.: Remarks on modification of Helgason’s support theorem. II. Proc. Japan Acad., 77A , 87-91 (2001). · Zbl 0991.44001 · doi:10.3792/pjaa.77.87
[6] Zalcman, L.: Uniqueness and nonuniqueness for the Radon transform. Bull. London Math. Soc., 14 , 241-245 (1982). · Zbl 0464.28006 · doi:10.1112/blms/14.3.241
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