If λ is a positive vector measure on _l_2, 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 _L_2(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 _L_2(λ) that we call the selfweighted approximation. As an application, we show a new extrapolation technique.
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Luis M. García-Raffi, Damián Ginestar, Enrique A. Sánchez Pérez, Vector Measure Orthonormal Systems and Self-weighted Functions Approximation. Publ. Res. Inst. Math. Sci. 41 (2005), no. 3, pp. 551–563DOI 10.2977/PRIMS/1145475222