Fundamental operations (reciprocal, integral, derivative) on Walsh function series representations of functions with discontinuities are defined.
Vanishing wavelet moments (the cancellation property) lead to sparse representations of functions and operators.
We use the potential theory to give integral representations of functions in the Sobolev spaces, where and is a smooth bounded domain in.
The emphasis on hierarchical representations of functions on intervals helps to address issues of both high-order approximation and efficient application of integral operators, and the lack of regularity of multiwavelets does not preclude their use in representing differential operators.
The application of wavelets for the numerical solution of differential equations has several advantages, namely: Vanishing wavelet moments (the cancellation property) lead to sparse representations of functions and operators.
where is eigenvalue of the matrix The integration over the variable comes from using an alternate representation of function [12].
The European Society for Surgery of the Shoulder and Elbow (ESSSE) recommends pain-limited ROM as a better representation of function in patients with shoulder disorders [ 61].
However, the models purporting to explain structural radiation generally use simplistic representations of selectable function.
The following result provides an integral representation of functions belonging to the class S b ∗.
We begin by presenting an integral representation of functions belonging to the class MS p.
