Fractal Functions and Wavelet Expansions Based on Several Scaling Functions

We present a method for constructing translation and dilation invariant functions spaces using fractal functions defined by a certain class of iterated function systems. These spaces generalize the C0 function spaces constructed in [D. Hardin, B. Kessler, and P. R. Massopust, J. Approx. Theory71 (1992), 104-120] including, for instance, arbitrarily smooth function spaces. These new function spaces are generated by several scaling functions and their integer-translates. We give necessary and sufficient conditions for these function spaces to form a multiresolution analysis of L2R.