Admissible Designs for Polynomial Spline Regression

Given f = (f sub o,...,f sub m) on the closed interval a,b we consider the matrix M(mu) = integral (f'f d mu) for any probability measure mu on the closed interval a,b. The measure mu is called admissible if there does not exist a nu such that M(nu) - M(mu) is positive semi-definite and not equal to 0. A theorem is given.