A method is presented to find an optimal lower bound on the quadratic functional integrals which appear in the derivation of bounds on the hadronic contribution to the muon magnetic moment, or on the $K_{l3\mathrm{}}$ form factors, when one knows that the function and its derivative take some definite values at the origin and that its phase is given on a part of the unitarity cut.

• Received 11 July 1972

DOI:https://doi.org/10.1103/PhysRevD.7.2136