The Symbol Series Expression and Holder Exponent Estimates of Fractal Interpolation Function

摘要

Now fractal interpolation functions (FIFs) are mainly described in terms of concrete interpolation region and its partition form. Many theory and applications only deal with low dimensional interpolation. In this paper, we consider a high dimensional fractal interpolation problem and describe a generalized definition of FIFs based on multiscale partition and refinable set. This definition enables us to investigate the expression with symbol series of FIFs under more general setting. By applying the expression with series of FIFs, we discuss Lipschitz continuity of FIR and give the estimates of Holder exponent of FIR. The obtained results can be easily applied to concrete fractal interpolation problems.