Affine fractal functions as bases of continuous funtions

Abstract

The objective of the present paper is the study of affine transformations of the plane, which provide self-affine curves as attractors. The properties of these curves depend decisively of the coefficients of the system of affinities involved. The corresponding functions are continuous on a compact interval. If the scale factors are properly chosen one can define Schauder bases of C[a; b] composed by affine fractal functions close to polygonals. They can be chosen bounded. The basis constants and the biorthogonal sequence of coefficient functionals are studied.

Keywords: Fractal interpolation functions, iterated function systems, Schauder bases.

Quaestiones Mathematicae 37(2014), 415–428