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Remarks on the paper 'Transient Markov convolution semi-groups and the associated negative definite functions'
- Source :
- Nagoya Math. J. 102 (1986), 181-184
- Publication Year :
- 1986
- Publisher :
- Cambridge University Press (CUP), 1986.
-
Abstract
- 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 followingTheorem. 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.
Details
- ISSN :
- 21526842 and 00277630
- Volume :
- 102
- Database :
- OpenAIRE
- Journal :
- Nagoya Mathematical Journal
- Accession number :
- edsair.doi.dedup.....ee71b09afcdce85c92c9b4f44d7989ca