Convolution in perfect Lie groups
2016 ◽
Vol 161
(1)
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pp. 31-45
Keyword(s):
Open Set
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AbstractLetGbe a connected perfect real Lie group. We show that there exists α < dimGandp∈$\mathbb{N}$* such that if μ is a compactly supported α-Frostman Borel measure onG, then thepth convolution power μ*pis absolutely continuous with respect to the Haar measure onG, with arbitrarily smooth density. As an application, we obtain that ifA⊂Gis a Borel set with Hausdorff dimension at least α, then thep-fold product setApcontains a non-empty open set.
2013 ◽
Vol 95
(3)
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pp. 362-382
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Keyword(s):
2006 ◽
Vol 58
(4)
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pp. 691-725
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1985 ◽
Vol 38
(1)
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pp. 55-64
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Keyword(s):
2013 ◽
Vol 2013
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pp. 1-13
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2013 ◽
Vol 12
(08)
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pp. 1350055
2013 ◽
Vol 10
(07)
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pp. 1320011
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Keyword(s):
2002 ◽
Vol 31
(1)
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pp. 11-21
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Keyword(s):
2007 ◽
Vol 18
(07)
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pp. 783-795
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Keyword(s):