Z. Mouayn, Department of Mathematics, Faculty of Sciences and Technics (M'Ghila), Cadi Ayyad University, BP 523, Beni Mellal, Morocco, e-mail: mouayn@math.net
Abstract: We give an explicit expression of a two-parameter family of Flensted-Jensen's functions $\Psi_{\mu,\alpha}$ on a concrete realization of the universal covering group of $U(1,1)$. We prove that these functions are, up to a phase factor, radial eigenfunctions of the Landau Hamiltonian on the hyperbolic disc with a magnetic field strength proportional to $\mu$, and corresponding to the eigenvalue $4\alpha( \alpha-1)$.
Keywords: Flensted-Jensen's functions, universal covering group, Landau Hamiltonian, hyperbolic disc
Classification (MSC 2000): 33C05, 35J10, 35Q40, 43A90, 57M10, 58C40
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