  When considering a charged particle evolving in the Poincar\'e disk under
influence of a uniform magnetic field with a strength proportional to +1, we
construct for all hyperbolic Landau level \epsilon^\gamma_$m$ m = 4m(-m), m 2
Z+ \[0, /2] a family of coherent states transforms labeled by (,m) and mapping
isometrically square integrable functions on the unit circle with respect to
the measure sin^\gamma-2m (\theta/2) d\theta onto spaces of bound states of the
particle. These transforms are called circular Bargmann transforms.
