An Example of a Solvable Lie Group Admitting an Absolutely Continuous Gauss Semigroup with Incomparable Supports

M. McCrudden
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M. McCrudden: University of Manchester, Department of Mathematics

A chapter in Probability Measures on Groups X, 1991, pp 293-297 from Springer

Abstract: Abstract For any locally compact group G let P(G) denote the topological semigroup of probability (Borei) measures on G, where P(G) has the weak topology and the operation is convolution of measures. Recall that a Gauss semigroup on G is a homomorphism t ↦ μ t of ℝ + * (positive reals under addition) into P(G) such that (i) no μt is a point measure (ii) for each neighbourhood V of 1 ∈ G, we have % MathType!MTEF!2!1!+- % feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aIXaaabaGaamiDaaaacqaH8oqBdaWgaaWcbaGaamiDaaqabaGccaGG % OaGaam4raiaacYfacaWGwbGaaiykaiabgkziUkaaicdacaWGHbGaam % 4CaiaadshacqGHtgYRcaaIWaaaaa!46A2! $$ \frac{1}{t}{\mu _t}(G\backslash V) \to 0ast \downarrow 0 $$ .

Keywords: Support Behaviour; Topological Semigroup; Lecture Note Math; Invariant Subalgebra; Diagonal Subalgebra (search for similar items in EconPapers)
Date: 1991
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DOI: 10.1007/978-1-4899-2364-6_21

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