POISSON SPACES FOR PROPER SEMIGROUPS OF SEMI-SIMPLE LIE GROUPS
2007 ◽
Vol 07
(03)
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pp. 273-297
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Keyword(s):
Let ν be a probability measure on a semi-simple Lie group G with finite center. Under the hypothesis that the semigroup S generated by ν has non-empty interior, we identify the Poisson space Π = G/MνAN, where bounded (l.u.c.) ν-harmonic functions in G have a one-to-one correspondence with measurable (continuous) functions in Π. This paper extends a classical result (see Furstenberg [7], Azencott [1] and others), where the semigroup generated by ν was assumed to be the whole (connected) group. We present two detailed examples.
2020 ◽
Vol 58
(4)
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pp. 477-496
1983 ◽
Vol 93
(3-4)
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pp. 181-188
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2013 ◽
Vol 95
(3)
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pp. 362-382
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Keyword(s):
1992 ◽
Vol 112
(1)
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pp. 91-108
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Keyword(s):
Keyword(s):
1985 ◽
Vol 38
(1)
◽
pp. 55-64
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Keyword(s):
2013 ◽
Vol 2013
◽
pp. 1-13
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