Resumen de Fractal approximation of a function from a countable sample set and associated fractal operator

P. Viswanathan

• In the literature of fractal approximation theory, the notion of fractal interpolation function is used to construct a family of fractal functions, called the α-fractal functions, corresponding to a fixed real-valued continuous function on a compact interval. The said α-fractal function that simultaneously interpolates and approximates a prescribed continuous function is established using a finite set of sampled values of the original function. Closer in this spirit, this note aims to enunciate the fractal approximate reconstruction of a continuous function from a countably infinite sample set. Some elementary properties of the fractal operator that maps the given Lipschitz continuous function to the reconstructed fractal counterpart is expounded from the view point of perturbation theory of operators. This may act as a first step to perceive the notion of fractal operator beyond the familiar terrain of bounded linear operators. Some sidelights are also presented.