Stability and linear independence associated with wavelet decompositions

Stability and Linear Independence Associated with Wavelet Decompositions

Wavelet decompositions are based on basis functions satisfying refinement equations. The stability, linear independence and orthogonality of the integer translates of basis functions play an essential role in the study of wavelets. In this paper we characterize these properties in terms of the mask sequence in the refinement equation satisfied by the basis function. AMS Subject Classifications:...

Stability and Linear Independence Associated with Scaling Vectors

In this paper, we discuss stability and linear independence of the integer translates of a scaling vector = (1 ; ; r) T , which satisses a matrix reenement equation (x) = n X k=0 P k (2x ? k); where (P k) is a nite matrix sequence. We call P (z) = 1 2 P P k z k the symbol of. Stable scaling vectors often serve as generators of multiresolution analyses (MRA) and therefore play an important role ...

Atomic Decompositions of Fuzzy Normed Linear Spaces for Wavelet Applications

Wavelet analysis is a powerful tool withmodern applications as diverse as: image processing, signal processing, data compression, data mining, speech recognition, computer graphics, etc. The aim of this paper is to introduce the concept of atomic decomposition of fuzzy normed linear spaces, which play a key role in the development of fuzzy wavelet theory. Atomic decompositions appeared in appli...

Factors associated with the functional independence level in older adults

Introduction: Functional independence in old age refers to active presence in daily life. One of the best ways to evaluate the functional independence of elderly is assessing the level of activities. This study aims to determine the status of functional independence in performing instrumental and daily activities as well as its related factors. Methods: This cross-sectional study was cond...

Cauchy-Rassias Stability of linear Mappings in Banach Modules Associated with a Generalized Jensen Type Mapping