Reproduction of Exponential Polynomials by Multivariate Non-stationary Subdivision Schemes with a General Dilation Matrix

TL;DR

This paper characterizes how multivariate non-stationary subdivision schemes with general dilation matrices can reproduce exponential polynomials, providing algebraic conditions for checking and designing schemes with specific reproduction properties.

Contribution

It introduces algebraic conditions on scheme symbols that determine their ability to reproduce exponential polynomials, aiding in the construction of schemes with desired properties.

Findings

Algebraic conditions for reproduction capabilities

Tools for checking existing schemes

Examples illustrating the theoretical results

Abstract

We study scalar multivariate non-stationary subdivision schemes with a general dilation matrix. We characterize the capability of such schemes to reproduce exponential polynomials in terms of simple algebraic conditions on their symbols. These algebraic conditions provide a useful theoretical tool for checking the reproduction properties of existing schemes and for constructing new schemes with desired reproduction capabilities and other enhanced properties. We illustrate our results with several examples.