| We study dimension properties of some continuous functions of the form g(t) = ;An IFS is an iterative procedure which starts from a function f and produces a limit object, the attractor g. The functions f and g are then related by a functional equation f(t) = (1 ;The iterative nature of an IFS makes it particularly well-suited for studying dimension problems. We obtain a general formula for the dimension of the graph of g under an apriori assumption on the oscillation of g, thus generalizing several previously known results.;To decide when this apriori assumption on g is satisfied, we study the functional equation relating f and g. We give precise conditions in terms of the asymptotic variance on the given function f for the solution g to be in certain smoothness classes. The method we use for studying this functional equation utilizes some recent, discrete decomposition techniques from harmonic analysis. More specifically, we use the... |
