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Planar Convex Bodies with a Common Directed X-ray
Butchler, Gene Lacy
Medin, Ashley
Solmon, Donald C.
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.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
37 (2005)
Subjects
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.
Languages
en
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