On degenerate multi-dimensional dispersion laws

Degeneration of multi-dimensional dispersion laws analytic in the vicinity of zero is investigated under the assumption that the corresponding degeneracy function satisfies a definite condition (Eq. (3)). It is proved that only two-dimensional dispersion laws ω(p, q), whose asymptotic behavior at small p and q has some definite form (Eq. (28)), can be degenerate with respect to the decay process 1 → 2. It is shown that the corresponding degeneracy function is unique and its asymptotic behavior is found. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 112, No. 1, pp. 124–131.