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Remarks on the paper “Transient Markov convolution semi-groups and the associated negative definite functions”
Published online by Cambridge University Press: 22 January 2016
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Let X be a locally compact and σ-compact abelian group and let denote the dual group of X. We denote by ξ a fixed Haar measure on X and by the Haar measure associated with ξ. In [2], we show the following
Theorem. Let (αt)t≧0 be a sub-Markov convolution semi-group on X and let ψ be the negative definite function associated with (αt)t≧0. Then (αt)t≧0 is transient if and only if Re (1/ψ) is locally -summable.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1986
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