Distance to the convex hull of an orbit under the action of a compact Lie group
1999 ◽
Vol 66
(3)
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pp. 331-357
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Keyword(s):
AbstractFor a real vector space V acted on by a group K and fixed x and y in V, we consider the problem of finding the minimum (respectively, maximum) distance, relative to a K-invariant convex function on V, between x and elements of the convex hull of the K-orbit of y. We solve this problem in the case where V is a Euclidean space and K is a finite reflection group acting on V. Then we use this result to obtain an analogous result in the case where K is a maximal compact subgroup of a reductive group G with adjoint action on the vector component ρ of a Cartan decomposition of Lie G. Our results generalize results of Li and Tsing and of Cheng concerning distances to the convex hulls of matrix orbits.
1987 ◽
Vol 106
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pp. 121-142
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2009 ◽
Vol 8
(2)
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pp. 209-259
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2008 ◽
Vol 144
(1)
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pp. 163-185
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2010 ◽
Vol 147
(1)
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pp. 263-283
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1992 ◽
Vol 44
(6)
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pp. 1220-1240
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Keyword(s):
2006 ◽
Vol 182
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pp. 135-170
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1997 ◽
Vol 62
(2)
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pp. 160-174
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