  Functional and linear-algebraic approaches to the Delsarte problem of upper
bounds on codes are discussed. We show that Christoffel-Darboux kernels and
Levenshtein polynomials related to them arise as stationary points of the
moment functionals of some distributions. We also show that they can be derived
as eigenfunctions of the Jacobi operator. This motivates the choice of
polynomials used to derive linear programming upper bounds on codes in
homogeneous spaces.
