CHRISTOFFEL FUNCTIONS AND FINITE MOMENT PROBLEMS

The Christoffel functions are used here to approximate an unknown probability density u : [0, 1] --> R(+) whose first m moments mu(1),...,mu(m) only are available. We obtain a sequence u((m)) of estimators which (theoretically) converges to u. We test it in several numerical examples and compare u((m)) with the probability density which matches the given moments and minimizes the functional S-w(u) = - integral(0)(1) ln u dx/root x(1-x).