Abstract
In this note, we explain how we reached to an explicitly given second order difference operator in the study of the “representation theory” of the quantum SU(1,1) group of “non-compact type”. We set up a situation of functional analysis in which the operator is claimed to be self-adjoint, and the spectral analysis of the operator is disccussed. The “eigenfunctions” are explicitly given in terms of the basic hypergeometric functions. We then also discuss about an explicit spectral expansion theorem which corresponds to the Fok-Mehler formula in the “classical situation ”.
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© 1993 Springer Science+Business Media Dordrecht
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Kakehi, T., Masuda, T., Ueno, K. (1993). Spectrum of an operator appears in the quantum SU(1,1) group. In: Araki, H., Ito, K.R., Kishimoto, A., Ojima, I. (eds) Quantum and Non-Commutative Analysis. Mathematical Physics Studies, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2823-2_19
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DOI: https://doi.org/10.1007/978-94-017-2823-2_19
Publisher Name: Springer, Dordrecht
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