Takiguchi, Takashi Remarks on modification of Helgason’s support theorem. II. (English) Zbl 0991.44001 Proc. Japan Acad., Ser. A 77, No. 6, 87-91 (2001). [For part I see J. Inverse Ill-Posed Probl. 8, No. 5, 573-579 (2000; Zbl 0979.44001).]A modification of Helgason’s support theorem for the hyperplane Radon transform in \(R^n\) is discussed. Important results related to this theorem are due to J. Boman. Reviewer: Boris Rubin (Jerusalem) Cited in 1 ReviewCited in 3 Documents MSC: 44A12 Radon transform 30E10 Approximation in the complex plane Keywords:Radon transform; support theorem; Helgason’s support theorem; hyperplane Radon transform Citations:Zbl 0979.44001 PDF BibTeX XML Cite \textit{T. Takiguchi}, Proc. Japan Acad., Ser. A 77, No. 6, 87--91 (2001; Zbl 0991.44001) Full Text: DOI OpenURL References: [1] Arakelian, N. U.: Uniform approximation on closed sets by entire functions. Izv. Akad. Nauk SSSR Ser. Mat., 28 , 1187-1206 (1964) (in Russian). [2] Boman, J.: A local vanishing theorem for distributions. C. R. Acad. Sci. Paris, 315 , 1231-1234 (1992). · Zbl 0785.46039 [3] Boman, J.: Holmgren’s uniqueness theorem and support theorems for real analytic Radon transforms. Contemp. Math., 140 , 23-30 (1992). · Zbl 0791.44003 [4] Boman, J.: Uniqueness and non-uniqueness for microanalytic continuation of ultradistributions. Contemp. Math., 251 , 61-82 (2000). · Zbl 0957.35008 [5] Fuchs, W. H. J.: Théorie de l’Approximation des Fonctions d’une Variable Complexe. Las Presses de l’Université de Montréal, Montréal (1968). · Zbl 0199.39701 [6] Helgason, S.: Gropes and Geometric Analysis. Academic Press, Orlando-San Diego-San Francisco-New York-London-Toronto-Montreal-Sydney-Tokyo-São Paulo (1984). · Zbl 0543.58001 [7] Hörmander, L.: The Analysis of Linear Partial Differential Operators. Vol. I. Springer, Berlin-Heidelberg-New York-London-Paris-Tokyo-Hong Kong (1983). · Zbl 0521.35002 [8] Kaneko, A.: Remarks on hyperfunctions with analytic parameters. J. Fac. Sci. Univ. Tokyo, 22 , 371-407 (1975). · Zbl 0319.46027 [9] Kaneko, A.: Introduction to Hyperfunctions. Kluwer, Dordrecht-Boston (1988). · Zbl 0687.46027 [10] Takiguchi, T.: Remarks on modification of Helgason’s support theorem. J. Inv. Ill-posed Prob., 8 , 573-579 (2000). · Zbl 0979.44001 [11] Takiguchi, T., and Kaneko, A.: Radon transform of hyperfunctions and support theorem. Hokkaido Math. J., 24 , 63-103 (1995). · Zbl 0828.46040 [12] Tanabe, S., and Takiguchi, T.: A local vanishing theorem for ultradistributions with analytic parameters. J. Fac. Sci. Univ. Tokyo, 40 , 607-621 (1993). · Zbl 0811.46035 [13] Zalcman, L.: Uniqueness and nonuniqueness for the Radon transform. Bull. London. Math. Soc., 14 , 241-245 (1981). · Zbl 0464.28006 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.