The Delsarte Method in the Problem of the Antipodal Contact Numbers of Euclidean Spaces of High Dimensions

We study the Delsarte problem for even functions continuous on [-1,1], nonpositive on [-1/2,1/2], and representable as series with respect to the ultraspherical polynomials. The value of the Delsarte problem gives an upper bound for the largest power of antipodal spherical 1/2-code of the space Rm.