Legendre transform of sampled signals by fractal methods (Q2906707)

The authors present a fractal method of computing the Legendre expansion for a sample signal without periodicity, but with a single hypothesis of continuity. The computation of the Legendre transform and the series expansion for real sampled signals is executed via an affine fractal interpolation by choosing a scale vector. Pointwise, uniform and mean-square convergences of the constructed Legendre expansion are proved. This enables a representation and an evaluation of the signal in the case that the step and the expansion-order are suitably chosen.NEWLINENEWLINEFor the entire collection see [Zbl 1239.00060].