Superluminal transoformations and tachyons

In this paper real superluminal transformations are studied assuming the existence of the superluminal or f-world which is completely symmetrical to the subluminal or s-world. The basic assumption is that if a reference frame Ssub(f) is superluminal with respect to a subluminal reference frame Ssub(s), then Ssub(f) must be superluminal to all subluminal reference frame S'sub(s). From this assumption two types of superluminal transformations, Msub(+-) and Nsub(+-), are derived. However, under transformations Msub(+-) the light velocity is in general not invariant, while for Nsub(+-) the relative velocity of frames Ssub(f) and Ssub(s) has not an evident physical meaning. Other properties of both transformations are briefly discussed and rather pessimistic conclusions concerning the validity of the duality principle are reached