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Zbl 1087.81034
Lindsay, J.Martin
Integral-sum kernel operators. (English)
[A] Attal, Stephane (ed.) et al., Quantum probability communications. Vol XII. Lectures from the Grenoble summer school, Grenoble, France, June 1998. River Edge, NJ: World Scientific. QP-PQ: Quantum Probability and White Noise Analysis 12, 1-21 (2003). ISBN 981-238-427-8/hbk; ISBN 981-238-959-8/pbk; ISBN 981-238-428-6/set

These notes consist of an introduction to A. Guichardet's functor which allows to induce from the structure on a set structure on the finite power set; a re-examination of I. E. Segal's notion of duality endowing Fock space with (quantum) probabilistio interpretation and algebraic structure; and an exposition of integral-sum kernel operators, as mixed multiple quantum Wiener integrals, extending H. Maassen's original idea and P.-A. Meyer's complenent. The author suggests to use sone primitive cohomology to derive some sharp estimates. These notes might serve as an induction to the new approach 10 quantum stochastic calculus developed by S. Attal and the author, and also to W. von Waldenfels' recent application of integral-sum kernel operators to physical models.
[Stanisław Wedrychowicz (Rzeszów)]

MSC 2000:: *81S25 Quantum stochastic calculus

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