Examples and counterexamples regarding hyperfinite representations of real distributions

Examples and counterexamples regarding hyperfinite representations of real distributions

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 Lp norm, and we study the failure of an...

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Veröffentlicht in:Examples and counterexamples 2022-11, Vol.2, p.100061, Article 100061
1. Verfasser: Bottazzi, Emanuele
Format: Artikel
Sprache:eng
Schlagworte:
Generalized functions
Nonstandard analysis
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Zusammenfassung: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 Lp norm, 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.
ISSN:2666-657X
2666-657X
DOI:10.1016/j.exco.2022.100061