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Convolution semigroups of states.

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Convolution semigroups of states. / Lindsay, Martin; Skalski, Adam G.

In: Mathematische Zeitschrift, Vol. 267, No. 1-2, 02.2011, p. 325-339.

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Lindsay, M & Skalski, AG 2011, 'Convolution semigroups of states.', Mathematische Zeitschrift, vol. 267, no. 1-2, pp. 325-339. https://doi.org/10.1007/s00209-009-0621-9

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Lindsay, Martin ; Skalski, Adam G. / Convolution semigroups of states. In: Mathematische Zeitschrift. 2011 ; Vol. 267, No. 1-2. pp. 325-339.

Bibtex

@article{faf5a21bb0c6483faac9fc6d2904537f,
title = "Convolution semigroups of states.",
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.",
keywords = "Convolution, quantum group, C*-bialgebra, disrete semigroup, quantum L\'evy process.",
author = "Martin Lindsay and Skalski, {Adam G.}",
note = "15 pages. Preprint, 24 June 2009. Published Online First{\texttrademark}, 3 November 2009. The original publication is available at www.springerlink.com",
year = "2011",
month = feb,
doi = "10.1007/s00209-009-0621-9",
language = "English",
volume = "267",
pages = "325--339",
journal = "Mathematische Zeitschrift",
issn = "0025-5874",
publisher = "Springer New York",
number = "1-2",

}

RIS

TY - JOUR

T1 - Convolution semigroups of states.

AU - Lindsay, Martin

AU - Skalski, Adam G.

N1 - 15 pages. Preprint, 24 June 2009. Published Online First™, 3 November 2009. The original publication is available at www.springerlink.com

PY - 2011/2

Y1 - 2011/2

N2 - 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.

AB - 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.

KW - Convolution

KW - quantum group

KW - C-bialgebra

KW - disrete semigroup

KW - quantum L\'evy process.

U2 - 10.1007/s00209-009-0621-9

DO - 10.1007/s00209-009-0621-9

M3 - Journal article

VL - 267

SP - 325

EP - 339

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

SN - 0025-5874

IS - 1-2

ER -