We introduce a polynomial spectral calculus that follows from the summation by parts property of the Legendre-Gauss-Lobatto quadrature. We use the calculus to simplify the analysis of two multidimensional discontinuous Galerkin spectral element approximations.
@article{arxiv.1704.00709,
title = {A Polynomial Spectral Calculus for Analysis of DG Spectral Element Methods},
author = {David A. Kopriva},
journal= {arXiv preprint arXiv:1704.00709},
year = {2017}
}