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On the closure of spaces of sums of Ridge functions and the range of the X-ray transform. (English) Zbl 0521.46018


MSC:

46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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References:

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[2] K.J. FALCONER, Consistency conditions for a finite set of projections of a function, Math. Proc. Cambridge Philos. Soc., 85 (1979), 61-68.0386.2800880e:28010 · Zbl 0386.28008
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[9] K.T. SMITH, D.C. SOLMON, S.L. WAGNER, Practical and mathematical aspects of the problem of reconstructing objects from radiographs, Bull. A.M.S., 83 (1977), 1227-1270.0521.6509058 #9394a · Zbl 0521.65090
[10] L. SVENSSON, When is the sum of closed subspaces closed? An example arising in computerized tomography, Research Report, Royal Inst. Technology (Stockholm), 1980.
[11] J.V. LEAHY, K.T. SMITH, D.C. SOLMON, Uniqueness, nonuniqueness and inversion in the X-ray and Radon problems, to appear in Proc. Internat. Symp. on III-posed Problems, Univ. of Delaware, Newark, Delaware, 1979.
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