Abstract
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 in L2(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 subspaces Vk, k∈Z, consisting of certain CHFIFs in L2(R)∩C0(R).
Highlights
The theory of multiresolution analysis provides a powerful method to construct wavelets having far reaching applications in analyzing signals and images [1, 2]
The availability of a larger set of free variables and constrained variables with Coalescence Hidden-variable Fractal Interpolation Functions (CHFIFs) in multiresolution analysis based on CHFIFs provides more control in reconstruction of functions in L2(R) than that provided by multiresolution analysis based only on Affine Fractal Interpolation Functions (AFIFs)
The availability of a larger set of free variables and constrained variables in our multiresolution analysis based on CHFIFs provides more control in reconstruction of functions in L2(R) than that provided by multiresolution analysis based only on affine FIFs
Summary
The theory of multiresolution analysis provides a powerful method to construct wavelets having far reaching applications in analyzing signals and images [1, 2]. In [8], multiresolution analysis of L2(R) was generated from certain classes of Affine Fractal Interpolation Functions (AFIFs). Such results were generalized to several dimensions in [9, 10]. The details on implementation of recent work on multiresolution analysis with AFIF bases can be found in [17]. In the present work, such a multiresolution analysis using CHFIFs as basis functions is developed. The multiresolution analysis of L2(R) is carried out in terms of nested sequences of vector subspaces Vk, k ∈ Z
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
