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

Pierre Bieliavsky, Axel de Goursac, Yoshiaki Maeda, Florian Spinnler

    Research output: Contribution to journalArticlepeer-review


    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 associated to this natural star-product. As an application, we prove a new identity on Bessel functions.

    Original languageEnglish
    Pages (from-to)362-402
    Number of pages41
    JournalAdvances in Mathematics
    Publication statusPublished - 2016 Mar 19


    • Bessel functions
    • Deformation quantization
    • Orthogonality relation
    • Principal series
    • Star-exponential
    • Unitary representation

    ASJC Scopus subject areas

    • Mathematics(all)


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