The relativistic semigroup,the Lorentz group,and tachyons. III

The construction of a linear, isomorphic, bounded realization of a tachyon semigroup (TSG) is carried out on a dual pair of space-times in which the sought realization by a parametric group is a semigroup of relativistic endomorphisms. The found relativistic semigroup of dual space-time transformations possesses definite probability-theoretical properties.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, July, 1977.The author is indebted to D. D. Ivanenko for his discussion, attention, and support.