On degenerate multidimensional dispersion laws

We study degeneration of multidimensional analytic at the vicinity dispersion laws given that the corresponding function of degeneracy satisfies condition (3). We prove that two-dimensional dispersion laws $\omega(p,q)$ can be degenerate with respect to the decay process $1\to2$ if and only if their asymptotic behaviour when $p$ and $q$ are small has the form (28). It is shown that the corresponding function of degeneracy is unique and its asymptotic behaviour is found.