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Fourier transform of random variables associated with the multi-dimensional Heisenberg Lie algebra


Authors: Luigi Accardi and Andreas Boukas
Journal: Proc. Amer. Math. Soc. 143 (2015), 4095-4101
MSC (2010): Primary 60B15, 81R05
DOI: https://doi.org/10.1090/proc/12539
Published electronically: April 6, 2015
MathSciNet review: 3359597
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Abstract | References | Similar Articles | Additional Information

Abstract: We compute the Fourier transform (or vacuum characteristic function) of quantum random variables (observables), defined as self-adjoint finite sums of Fock space operators, satisfying the multi-dimensional Heisenberg Lie algebra commutation relations. The main tool is a splitting formula for the multi-dimensional Heisenberg group obtained by Feinsilver and Pap.


References [Enhancements On Off] (What's this?)

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  • [2] Philip Feinsilver and René Schott, Algebraic structures and operator calculus. Vol. I, Mathematics and its Applications, vol. 241, Kluwer Academic Publishers Group, Dordrecht, 1993. Representations and probability theory. MR 1227095 (94j:22024)
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Additional Information

Luigi Accardi
Affiliation: Centro Vito Volterra, Università di Roma Tor Vergata, via Columbia 2, 00133 Roma, Italy
Email: accardi@volterra.mat.uniroma2.it

Andreas Boukas
Affiliation: Centro Vito Volterra, Università di Roma Tor Vergata, via Columbia 2, 00133 Roma, Italy
Email: andreasboukas@yahoo.com

DOI: https://doi.org/10.1090/proc/12539
Keywords: Bochner's theorem, vacuum characteristic function, Fock space, quantum random variable, multi-dimensional Heisenberg algebra
Received by editor(s): November 15, 2013
Received by editor(s) in revised form: May 6, 2014
Published electronically: April 6, 2015
Additional Notes: This work is supported by the RSF grant 14-11-00687, Steklov Mathematical Institute.
Communicated by: Sergei K. Suslov
Article copyright: © Copyright 2015 American Mathematical Society

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