Abstract
Some of the conditions under which the solutions of an infinite-component wave equation form a complete set are investigated. The investigation is carried out by the resolvent method, and this allows us to find a connection between the NO-GO theorem and the existence or not of the operator exp [πK3]. As a concrete example the completeness relation is explicitly worked out for the solutions of an equation with a linear mass spectrum; as a consequence of the imposed conditions it is found that the intercept of the trajectory must be −1/2. The two Majorana representations are considered, and it is found that completeness holds for the bosonic case only. In this last case it is shown that to the completeness contribute a discrete set of timelike states and a continuum of states with complex energy.
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