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Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics >
Rendiconti dell' Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.37 (2005) >
Please use this identifier to cite or link to this item:
http://hdl.handle.net/10077/4150
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| Title: | Planar Convex Bodies with a Common Directed X-ray |
| Authors: | Butchler, Gene Lacy
Medin, Ashley
Solmon, Donald C. |
| Keywords: | Directed X-ray
Convex body |
| Issue Date: | 2005 |
| Publisher: | Università degli Studi di Trieste. Dipartimento di Matematica e Informatica |
| Citation: | G. L. Butcher, A. Medin, D. C. Solmon, "Planar Convex Bodies with a Common Directed X-ray", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 37 (2005), pp. 181-206. |
| Series/Report no.: | Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
37 (2005) |
| Abstract: | We study X(K), the set of convex bodies in the plane
with the same directed X-ray as the convex body K. We show that
X(K) is complete in the metrics of the uniform and Lp norms.
In fact these metrics turn out to be equivalent even though X(K)
is almost always infinite dimensional. In addition, we characterize the compact subsets of X(K) and determine necessary and
sufficient conditions for X(K) to be uniformly bounded. |
| URI: | http://hdl.handle.net/10077/4150 |
| ISSN: | 0049-4704 |
| MS Classification: | 52A10
52A38 |
| Appears in Collections: | Rendiconti dell' Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.37 (2005)
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