Abstract
Sequences of real functions that are orthogonal with respect to a vector measure are
a natural generalization of the orthogonal systems with respect to a parametric measure. In this paper we develop a new procedure to construct non linear approximations
of functions by de fining orthogonal series in spaces of square integrable functions with
respect to a vector measure which Fourier coefficients are also functions. We study the
convergence properties of these series, defi ning a convenient approximation structure for
signal processing involving time dependence of the measure. Some examples regarding
classical orthogonal polynomials are given.
