Sums of homogeneous functions and the range of the divergent beam x-ray transform
- 1 January 1983
- journal article
- research article
- Published by Taylor & Francis in Numerical Functional Analysis and Optimization
- Vol. 5 (4) , 363-419
- https://doi.org/10.1080/01630568308816147
Abstract
In this paper we analyze the divergent beam x-ray transform (and generalizations) with finite source set in as an operator between Lρspaces. The main results give conditions for this operator to have closed range when n = 2, 3 and give a characterization of the range. The dual result asserts closure in Lρ of sums of spaces of functions homogeneous of given degree from the several sources.Keywords
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