Starting from the Mandelstam representation with the strip approximation, an integral equation is obtained for the signature of partial-wave amplitudes. In addition to a long-range generalized potential, a short-range generalized potential is introduced here in order to express the effects from distant singularities. High-energy effects at low momentum transfers can be automatically taken into account, if one solves the integral equation by employing the above potentials in a finite strip. A method is proposed to express the short-range potential in terms of low-energy resonances in the direct channel. This method may simplify a complete bootstrap to calculate both the low-energy resonances and the asymptotic behaviour. As a preliminary application of our method, quantities like σ(∞),α′ P (0) andα ϱ (0) are calculated, by imposing the conditionsα P (0)=I and using the low-energy resonance parameters as inputs. Both σ(∞) andα′ P (0) are calculated without assuming one of them and are in qualitative agreement with high-energy experiments.