Sequences of real functions that are orthogonal with respect to a vector measure are a natural generalization of orthogonal systems with respect to a parametric measure. In this paper we develop a new procedure to construct non-linear approximations of functions by dening orthogonal series in spaces of square integrable functions with respect to a vector measure whose Fourier coecients are also functions. We study the convergence properties of such series, dening a convenient approximation procedure for signal processing involving time dependence of the measure. Some examples involving classical orthogonal polynomials are given.
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Luis M. García-Raffi, E. Jiménez Fernández, Enrique A. Sánchez Pérez, A Non-linear Approach to Signal Processing by Means of Vector Measure Orthogonal Functions. Publ. Res. Inst. Math. Sci. 49 (2013), no. 2, pp. 241–269DOI 10.4171/PRIMS/105