Please use this identifier to cite or link to this item:
http://hdl.handle.net/10077/4150
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 | Source: | 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. |
Type: | Article | URI: | http://hdl.handle.net/10077/4150 | ISSN: | 0049-4704 |
Appears in Collections: | Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.37 (2005) |
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ButcherMedinSolomonRendMat37.pdf | 354.64 kB | Adobe PDF | ![]() View/Open |
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