  It is proven that for each given two-field channel - called the
``t-channel''- with (off-shell) ``scattering angle'' $\Theta_t$, the four-point
Green's function of any scalar Quantum Fields satisfying the basic principles
of locality, spectral condition together with temperateness admits a
Laplace-type transform in the corresponding complex angular momentum variable
$\lambda_t$, dual to $\Theta_t$. This transform enjoys the following
properties: a) it is holomorphic in a half-plane of the form $Re \lambda_t >
m$, where m is a certain ``degree of temperateness'' of the fields considered,
b) it is in one-to-one (invertible) correspondence with the (off-shell)
``absorptive parts'' in the crossed two-field channels, c) it extrapolates in a
canonical way to complex values of the angular momentum the coefficients of the
(off-shell) t-channel partial-wave expansion of the Euclidean four-point
function of the fields. These properties are established for all space-time
dimensions d+1 with $d \ge 2$.
