Vector Measure Orthonormal Systems and Self-weighted Functions Approximation

If λ is a positive vector measure on l2, the notion of λ-orthonormal system of functions leads to a natural generalization of the relation between orthogonality and best approximation in Hilbert spaces for spaces L2(λ) of square integrable functions with respect to λ. We provide a vector orthogonality criterion that induces the definition of a particular projection on a subspace of L2(λ) that we call the selfweighted approximation. As an application, we show a new extrapolation technique. §