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| Volume 6 |
| Number 2 |
| pp. 281-303 |
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| Conically equivalent convex sets and applications |
| Elisa Caprari and Alberto Zaffaroni |
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| Abstract |
| Given a normed space X and a cone K ⊆ X, two closed, convex sets A and B in X * are said to be K-equivalent if the support functions of A and B coincide on K. We characterize the greatest set in an equivalence class, analyze the equivalence between two sets, find conditions for the existence and the uniqueness of a minimal set, extending previous results. We give some applications to the study of gauges of convex radiant sets and of cogauges of convex coradiant sets. Moreover we study the minimality of a second order hypodifferential. |
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| Key words |
Mathematices Subject Classification |
| convex sets, support function, convex radiant sets, Minkowski gauge, convex coradiant sets, cogauge, hypodifferentiable functions |
52A07, 52A30, 46B20, 49J52 |
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| Reference |
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| Copyright© 2010 Yokohama Publishers |
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