Unitarity and the Veneziano Representation

The conjecture that simple Veneziano-type formulas represent the zeroth-order approximation to certain strong-interaction amplitudes is investigated. With $\mathrm{Im}\alpha$ as a small parameter, the question of incorporating unitarity to next order is studied, and a simple example illustrating some of the features is constructed. The problem is posed in terms of partial-wave amplitudes; therefore, the partial-wave projection of the Veneziano formula is also discussed in some detail.