MPEJ Volume 4, No.2, 19pp Received: Dec 17, 1997, Revised: Mar 18, 1998, Accepted: May 14, 1998 N. Ripamonti Classical Limit of the Matrix Elements on Quantized Lobachevskii Plane ABSTRACT: It is proved that the matrix elements $\wh F_{n,n+k}$ between harmonic oscillator eigenvectors of any smooth observable in the quantized Lobachevskii plane converge to the Fourier coefficients $F_{k}$ of the corresponding classical observable $F(A,\phi)$ at the classical limit $n\to\infty, \hbar\to 0, n\hbar\to A$, $k$ fixed, where $A$, $\phi$ are the oscillator action-angle variables. The Wigner functions are then defined and, as a consequence of the above result, their convergence to $\delta(A-A_{0})e^{-ik\phi}$ at the classical limit is proved when computed on the harmonic oscillator eigenstates $n$ and $n+k$.