Support of Non-separable Multivariate Scaling Function

TL;DR

This paper proposes a method to estimate the support of multivariable scaling functions for arbitrary dilation matrices, enabling calculation of the function's values on a tight set based on support size.

Contribution

It introduces a novel approach to estimate the support of multivariable scaling functions for any dilation matrix, facilitating more precise computations.

Findings

Method effectively estimates support for arbitrary dilation matrices.

Allows calculation of scaling function values on a tight set.

Enhances understanding of multivariable scaling functions.

Abstract

We make an estimation of the support of a multivariable scaling function for an arbitrary dilation matrix. We give a method of calculating the values of the scaling function on a tight set using the knowledge of the size of the support.