Upper Bound for the Double Spectral Function in Potential Scattering

抄録

For potentials V(z) holomorphic in Rez>0 and bounded by
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we show that the double spectral “function” ρ(s, t) is ac ontinuous function of s and t s>0, t>0, and we obtain an upper bound for it. This upper bound shows clearly that the double integral of the Mandelstam representation in fact exists and defines an analytic function of s and t in two cut planes. We indicate how to generalize these results to the case when ρ(s, t) is no longer a function but a distribution.