Non-formal star-exponential on contracted one-sheeted hyperboloids

Bieliavsky, Pierre;Marcillaud de Goursac, Axel;Maeda, Yoshiaki;Spinnler, Florian
(2016) Advances in mathematics — Vol. 291, n° 1, p. 362-402 (2016)

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Authors
  • Bieliavsky, PierreUCLouvain
    Author
  • Marcillaud de Goursac, AxelUCLouvain
    Author
  • Maeda, YoshiakiUCLouvain
    Author
  • Spinnler, FlorianUCLouvain
    Author
Abstract
In this paper, we exhibit the non-formal star-exponential of the Lie group SL(2,R) realized geometrically on the curvature contraction of its one-sheeted hyperboloid orbits endowed with its natural non-formal star-product. It is done by a direct resolution of the defining equation of the star-exponential and produces an expression with Bessel functions. This yields a continuous group homomorphism from SL(2,R) into the von Neumann algebra of multipliers of the Hilbert algebra underlied by this natural star-product. As an application, we prove a new identity on Bessel functions.
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Bieliavsky, P., Marcillaud de Goursac, A., Maeda, Y., & Spinnler, F. (2016). Non-formal star-exponential on contracted one-sheeted hyperboloids. Advances in mathematics, 291(1), 362-402. https://doi.org/10.1016/j.aim.2015.12.026 (Original work published 2016)