  The solutions of the arbitrary-spin massless wave equations over ${\bf R}^1
\times H^3$ space are obtained using the generalized coherent states for the
Lorentz group. The use of these solutions for the construction of invariant
propagators of quantized massless fields with an arbitrary spin over the ${\bf
R}^1 \times H^3$ space is considered. The expression for the scalar propagator
is obtained in the explicit form.
