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Extending the set of quadratic exponential vectors. (English) Zbl 1208.81124

Ouerdiane, Habib (ed.) et al., Quantum probability and infinite dimensional analysis. Proceedings of the 29th conference, Hammamet, Tunisia, October 13–18, 2008. Hackensack, NJ: World Scientific (ISBN 978-981-4295-42-0/hbk; 978-981-4295-43-7/ebook). QP-PQ: Quantum Probability and White Noise Analysis 25, 262-266 (2010).
Summary: We extend the square of white noise algebra over the step functions on \(\mathbb R\) to the test function space \(L^2(\mathbb R^d)\cap l^\infty(\mathbb R^d)\), and we show that in the Fock representation the exponential vectors exist for all test functions bounded by \(\frac12\).
For the entire collection see [Zbl 1197.81034].

MSC:

81S25 Quantum stochastic calculus
46L53 Noncommutative probability and statistics
60H40 White noise theory
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