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{Quantum Algebras and q-Special Functions Related to Coherent States Maps of the Disc

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Abstract:

The quantum algebras generated by the coherent states maps of the disc are investigated. It is shown that the analytic realization of these algebras leads to a generalized analysis which includes standard analysis as well as q-analysis. The applications of the analysis to star-product quantizations and q-special functions theory are given. Among others the meromorphic continuation of the generalized basic hypergeometric series is found and a reproducing measure is constructed, when the series is treated as a reproducing kernel.

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Authors and Affiliations

  1. Warsaw University Branch in Bialystok, Institute of Physics, Lipowa 41, PL-15-424 Bialystok, Poland.¶E-mail: aodzijew@cksr.ac.bialystok.pl, , , , , , PL

    Anatol Odzijewicz

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  1. Anatol Odzijewicz
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Received: 4 April 1996 / Accepted: 29 June 1997

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Odzijewicz, A. {Quantum Algebras and q-Special Functions Related to Coherent States Maps of the Disc . Comm Math Phys 192, 183–215 (1998). https://doi.org/10.1007/s002200050296

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  • DOI: https://doi.org/10.1007/s002200050296

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