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Convolution semigroups of states.

Lindsay, Martin and Skalski, Adam G. (2011) Convolution semigroups of states. Mathematische Zeitschrift, 267 (1-2). pp. 325-339. ISSN 1432-1823

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    Abstract

    Convolution semigroups of states on a quantum group form the natural noncommutative analogue of convolution semigroups of probability measures on a locally compact group. Here we initiate a theory of weakly continuous convolution semigroups of functionals on a C*-bialgebra, the noncommutative counterpart of a locally compact semigroup. On locally compact quantum groups we obtain a bijective correspondence between such convolution semigroups and a class of C_0-semigroups of maps which we characterise. On C*-bialgebras of discrete type we show that all weakly continuous convolution semigroups of states are automatically norm-continuous. As an application we deduce a known characterisation of continuous conditionally positive-definite Hermitian functions on a compact group.

    Item Type: Article
    Journal or Publication Title: Mathematische Zeitschrift
    Additional Information: 15 pages. Preprint, 24 June 2009. Published Online First™, 3 November 2009. The original publication is available at www.springerlink.com
    Uncontrolled Keywords: Convolution ; quantum group ; C*-bialgebra ; disrete semigroup ; quantum L\'evy process.
    Subjects: Q Science > QA Mathematics
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 34522
    Deposited By: Professor J. Martin Lindsay
    Deposited On: 22 Nov 2010 09:32
    Refereed?: Yes
    Published?: Published
    Last Modified: 09 Oct 2013 13:14
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/34522

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