On spaces of fractal functions. (English) Zbl 0851.58027
Summary: We introduce linear spaces consisting of continuous functions whose graphs are the attractors of a special class of iterated function systems. We show that such spaces are finite dimensional and give the bases of these spaces in an implicit way. Given such a space, we discuss how to obtain a set of knots for which the Lagrange interpolation problem by the space is uniquely solvable.
MSC:
37B99 | Topological dynamics |
37C70 | Attractors and repellers of smooth dynamical systems and their topological structure |
57Q45 | Knots and links in high dimensions (PL-topology) (MSC2010) |