Fractal Haar system Original Research Article

The Haar system is an alternative to the classical Fourier bases, being particularly useful for the approximation of discontinuities. The article tackles the construction of a set of fractal functions close to the Haar set. The new system holds the property of constitution of bases of the Lebesgue spaces of pp-integrable functions on compact intervals. Likewise, the associated fractal series of a continuous function is uniformly convergent. The case p=2p=2 owns some peculiarities and is studied separately.