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 Lpnorm, and we study the failure of an e...
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| Format: | Article |
| Language: | English |
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Elsevier
2022-11-01
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| Series: | Examples and Counterexamples |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666657X22000076 |
| _version_ | 1811187339322458112 |
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| author | Emanuele Bottazzi |
| author_facet | Emanuele Bottazzi |
| author_sort | Emanuele Bottazzi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T14:00:36Z |
| format | Article |
| id | doaj.art-7c942554db7b42eabc96bc3000d56541 |
| institution | Directory Open Access Journal |
| issn | 2666-657X |
| language | English |
| last_indexed | 2024-04-11T14:00:36Z |
| publishDate | 2022-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Examples and Counterexamples |
| spelling | doaj.art-7c942554db7b42eabc96bc3000d565412022-12-22T04:20:08ZengElsevierExamples and Counterexamples2666-657X2022-11-012100061Examples and counterexamples regarding hyperfinite representations of real distributionsEmanuele Bottazzi0University of Pavia, ItalyWe 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.http://www.sciencedirect.com/science/article/pii/S2666657X22000076Nonstandard analysisGeneralized functions |
| spellingShingle | Emanuele Bottazzi Examples and counterexamples regarding hyperfinite representations of real distributions Examples and Counterexamples Nonstandard analysis Generalized functions |
| title | Examples and counterexamples regarding hyperfinite representations of real distributions |
| title_full | Examples and counterexamples regarding hyperfinite representations of real distributions |
| title_fullStr | Examples and counterexamples regarding hyperfinite representations of real distributions |
| title_full_unstemmed | Examples and counterexamples regarding hyperfinite representations of real distributions |
| title_short | Examples and counterexamples regarding hyperfinite representations of real distributions |
| title_sort | examples and counterexamples regarding hyperfinite representations of real distributions |
| topic | Nonstandard analysis Generalized functions |
| url | http://www.sciencedirect.com/science/article/pii/S2666657X22000076 |
| work_keys_str_mv | AT emanuelebottazzi examplesandcounterexamplesregardinghyperfiniterepresentationsofrealdistributions |