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arXiv · 1501.07491

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

Pierre Bieliavsky·Axel de Goursac·Yoshiaki Maeda·Florian Spinnler
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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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BibTeXRIS

Pierre Bieliavsky, Axel de Goursac, Yoshiaki Maeda, Florian Spinnler. 2015-05-05. Non-formal star-exponential on contracted one-sheeted hyperboloids. https://arxiv.org/abs/1501.07491

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