Olshanski spherical pairs of semigroups type
2019 ◽
Vol 22
(03)
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pp. 1950021
Keyword(s):
Let [Formula: see text] be the infinite semigroup, inductive limit of the increasing sequence of the semigroups [Formula: see text], where [Formula: see text] is the unitary group of matrices and [Formula: see text] is the semigroup of positive hermitian matrices. The main purpose of this work is twofold. First, we give a complete classification of spherical functions defined on [Formula: see text], by following a general approach introduced by Olshanski and Vershik.10 Second, we prove an integral representation for functions of positive-type analog to the Bochner–Godement theorem, and a Lévy–Khinchin formula for functions of negative type defined on [Formula: see text].
2011 ◽
Vol 63
(2)
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pp. 381-412
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Keyword(s):
2017 ◽
Vol 16
(10)
◽
pp. 1750197
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2016 ◽
Vol 31
(17)
◽
pp. 1650102
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2003 ◽
Vol 35
(6)
◽
pp. 1059-1076
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Keyword(s):