Fractal Haar system

Abstract: 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 -integrable functions on compact intervals. Likewise, the associated fractal series of a continuous function is uniformly convergent. The case owns some peculiarities and is studied separately. [Copyright &y& Elsevier]