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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: 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.


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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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