References
Floret, K.: On well-located subspaces of distribution-spaces. Math. Ann.221, 147–151 (1976)
Gelfand, I.M., Graev, M.I., Vilenkin, N.Ya.: Generalized functions. V. New York: Academic Press 1966
Hahn, M., Quinto, E.T.: Distances between measures from 1-dimensional projections as implied by continuity of the inverse Radon transform. Preprint 1983
Helgason, S.: The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds. Acta Math.113, 153–180 (1965)
Helgason, S.: The Radon transform. Boston: Birkhäuser 1980
Helgason, S.: Ranges of Radon transforms. Proc. Symp. Appl. Math.27, 63–70 (1982). Providence, RI: Amer. Math. Soc. 1983
Hertle, A.: Continuity of the Radon transform and its inverse on Euclidean space. Math. Z.184, 165–192 (1983)
Hörmander, L.: Linear partial differential operators. Berlin, Heidelberg, New York: Springer 1963
Jarchow, H.: Locally convex spaces. Stuttgart: Teubner 1981
Komatsu, H.: Ultradistributions. I. J. Fac. Sci. Univ. Tokyo, Sec. IA20, 25–105 (1973)
Louis, A.K.: Orthogonal function series expansion and the null space of the Radon transform. SIAM J. Math. Anal. (1983)
Louis, A.K.: Picture reconstruction from projections in restricted range. Math. Meth. Appl. Sci.2, 209–220 (1980)
Ludwig, D.: The Radon transform on Euclidean space. Comm. Pure Appl. Math.19, 49–81 (1966)
Marr, R.B.: On the reconstruction of a function on a circular domain from a sampling of its line integrals. J. Math. Anal. Appl.45, 357–374 (1974)
Natterer, F.: Computerized tomography with unknown sources. SIAM J. Appl. Math.43, 1201–1212 (1983)
Perry, R.M.: On reconstructing a function on the exterior of a disc from its Radon transform. J. Math. Appl.59, 324–341 (1977)
Pietsch, A.: Nukleare lokalkonvexe Räume. Berlin, Heidelberg, New York: Springer 1965
Quinto, E.T.: Null spaces for the classical and spherical Radon transforms. J. Math. Anal. Appl.90, 408–420 (1982)
Quinto, E.T.: Singular value decomposition and inversion methods for the exterior Radon transform and a spherical transform. To appear J. Math. Anal. Appl. (1983)
Schaefer, H.H.: Topological vector spaces. Berlin, Heidelberg, New York: Springer 1971
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Hertle, A. On the range of the radon transform and its dual. Math. Ann. 267, 91–99 (1984). https://doi.org/10.1007/BF01458472
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DOI: https://doi.org/10.1007/BF01458472