부산대학교 도서관

The following extremal problem is solved: Let O be an operator whose lowest-mass coupling is to the two particles A and B and is given by a form factor F which is analytic in a complex plane cut along a section L of the real line. Given values of F, at points not on L, and the partial-wave amplitudes for AB scattering in the channels with the same quantum numbers as O, over some portion of L, what is the optimal lower bound for a given positively weighted integral over L of the spectral function of O, consistent with the elastic and inelastic unitarity relations on L The solution involves a system of two inhomogeneous singular integral equations of the Muskhelishvili type, which can be reduced to a singular integral equation of the Fredholm type. The results are applied to establish an upper bound of 0.25 for the nucleon renormalization constant, using the strong-coupling constant and ..pi..N scattering data in the P/sub 11/ and S/sub 11/ channels up to a c.m. energy of 1.7 GeV. The bound indicates that the nucleon is at least 75% composite. (AIP)