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From algebraic to analytic double product integrals

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posted on 22.03.2007 by Robin Hudson
The algebraic theory of double product integrals and particularly its role in the quantisation of Lie bialgebras is described. When the underlying associative algebra is that of the Itˆo differentials of quantum stochastic calculus such product integrals are formally represented as operators which are infinite sums of iterated integrals in Fock space. In this paper we describe some of the analytic problems encountered in making such sums rigourously meaningful, as well as the expected properties of such analytic double product integrals.

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  • Science

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  • Mathematical Sciences

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182916 bytes

Citation

HUDSON, R.L., 2008. From algebraic to analytic double product integrals. IN: Belavkin, V.P. and Guta, M. Quantum Stochastics And Information: Statistics, Filtering and Control, University of Nottingham, UK, 15 – 22 July 2006. World Scientific Publishing Co., pp. 34 - 36.

Publication date

2007

Notes

This is a pre-print. It was published in the book, Quantum Stochastics And Information: Statistics, Filtering and Control, University of Nottingham, UK, 15 – 22 July 2006 [ © World Scientific Publishing Co.]. The publisher's website is at: http://www.worldscientific.com/

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en

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