Annihilation Operators for Exponential Spaces in Subdivision

TL;DR

This paper explores differential and difference operators that annihilate specific exponential function spaces in two variables, aiming to improve subdivision schemes for accurately representing surfaces with trigonometric and hyperbolic functions.

Contribution

It introduces new annihilation operators for exponential spaces, enhancing subdivision schemes' ability to preserve complex exponential functions in surface modeling.

Findings

Identifies properties of operators that annihilate exponential subspaces

Connects operator theory to subdivision scheme design

Enables exact surface representation with trigonometric and hyperbolic functions

Abstract

We investigate properties of differential and difference operators annihilating certain finite-dimensional subspaces of exponential functions in two variables that are connected to the representation of real-valued trigonometric and hyperbolic functions. Although exponential functions appear in a variety of contexts, the motivation behind this work comes from considering subdivision schemes with the capability of preserving those exponential functions required for an exact description of surfaces parametrized in terms of trigonometric and hyperbolic functions.