Multiresolution Analysis Based on Coalescence Hidden-Variable Fractal Interpolation Functions

摘要

Multiresolution analysis arising from Coalescence Hidden-variable Fractal Interpolation Functions (CHFIFs) is developed. The availability of a larger set of free variables and constrained variables with CHFIF in multiresolution analysis based on CHFIFs provides more control in reconstruction of functions inL2(R)than that provided by multiresolution analysis based only on Affine Fractal Interpolation Functions (AFIFs). Our approach consists of introduction of the vector space of CHFIFs, determination of its dimension and construction of Riesz bases of vector subspacesVk, k∈Z, consisting of certain CHFIFs inL2(R)∩C0(R).