Fourier transform of random variables associated with the multi-dimensional Heisenberg Lie algebra
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- by Luigi Accardi and Andreas Boukas PDF
- Proc. Amer. Math. Soc. 143 (2015), 4095-4101 Request permission
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
- Ph. Feinsilver and G. Pap, Calculation of Fourier transforms of a Brownian motion on the Heisenberg group using splitting formulas, J. Funct. Anal. 249 (2007), no. 1, 1–30. MR 2338852, DOI 10.1016/j.jfa.2007.05.002
- 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, DOI 10.1007/978-94-011-1648-0
- Kôsaku Yosida, Functional analysis, 6th ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 123, Springer-Verlag, Berlin-New York, 1980. MR 617913
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
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 4095-4101
- MSC (2010): Primary 60B15, 81R05
- DOI: https://doi.org/10.1090/proc/12539
- MathSciNet review: 3359597