Fourier Asymptotics of Statistically Self-Similar Measures.
From the concept of attractor of a family of contractive affine transformations in the Euclidean plane R2, we study the fractality property of the De Rham function and other singular functions wich derive from it. In particular, we show as fractals the strong negations called k-negations.
The methodology of fractal interpolation is very useful for processing experimental signals in order to extract their characteristics of complexity. We go further and prove that the Iterated Function System involved may also be used to obtain new approximants that are close to classical ones. In this work a classical function and a fractal function are combined to construct a new interpolant. The fractal function is first defined as a perturbation of a classical mapping. The additional condition...