Examples and counterexamples regarding hyperfinite representations of real distributions

Abstract

We provide some examples and counterexamples regarding hyperfinite representations of real distributions. We examine some hyperfinite representatives of the null distribution and of the Dirac distribution, we discuss hyperfinite representations of an infinite Lpnorm, and we study the failure of an energy inequality for the discrete Laplacian in dimension 1. These examples are relevant for the study of partial differential equations with hyperfinite techniques.

Keywords

• Nonstandard analysis
• Generalized functions