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Boman, Jan

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

Ann. Inst. Fourier 34, No. 1, 207-239 (1984).
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Cited in 2 Reviews
Cited in 3 Documents

MSC:

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

Keywords:

sums of Ridge functions; range of the X-ray transform; image reconstruction from projections; tomography; matrix-valued differential operator; Lipschitz curve; boundary has non-vanishing principal curvatures
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\textit{J. Boman}, Ann. Inst. Fourier 34, No. 1, 207--239 (1984; Zbl 0521.46018)
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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. · Zbl 0386.28008
[3] C. HAMAKER, D.C. SOLMON, The angles between the null spaces of X-rays, J Math. Anal. Appl., 62 (1978), 1-23. · Zbl 0437.45025
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[5] J.L. KELLEY, I. NAMIOKA, Linear topological spaces, Van Nostrand, 1963. · Zbl 0115.09902
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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. · 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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