caa a22 4500 445836431 CHVBK 20180317145331.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s00209-009-0621-9 doi (NATIONALLICENCE)springer-10.1007/s00209-009-0621-9 Convolution semigroups of states [Elektronische Daten] [J. Lindsay, Adam Skalski] 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. Springer-Verlag, 2009 Convolution nationallicence Quantum group nationallicence C *-bialgebra nationallicence Discrete semigroup nationallicence Quantum Lévy process nationallicence Lindsay J. Department of Mathematics and Statistics, Lancaster University, LA1 4YF, Lancaster, UK aut Skalski Adam Department of Mathematics and Statistics, Lancaster University, LA1 4YF, Lancaster, UK aut Mathematische Zeitschrift Springer-Verlag 267/1-2(2011-02-01), 325-339 0025-5874 267:1-2<325 2011 267 209 https://doi.org/10.1007/s00209-009-0621-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-009-0621-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lindsay J. Department of Mathematics and Statistics, Lancaster University, LA1 4YF, Lancaster, UK aut NATIONALLICENCE 700 1- Skalski Adam Department of Mathematics and Statistics, Lancaster University, LA1 4YF, Lancaster, UK aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 267/1-2(2011-02-01), 325-339 0025-5874 267:1-2<325 2011 267 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer