Multiplication product formula for associated homogeneous distributions on R
| dc.contributor.author | Franssens, G.R. | |
| dc.date | 2011 | |
| dc.date.accessioned | 2016-03-29T12:43:51Z | |
| dc.date.available | 2016-03-29T12:43:51Z | |
| dc.identifier.uri | https://orfeo.belnet.be/handle/internal/3078 | |
| dc.description | The set of associated homogeneous distributions (AHDs) on R, ℋ′(R), consists of the distributional analogues of power-log functions with domain in R. This set contains the majority of the (one-dimensional) distributions one typically encounters in physics applications. The recent work done by the author showed that the set ℋ′(R) admits a closed convolution structure (ℋ′(R), *). By combining this structure with the generalized convolution theorem, a distributional multiplication product was defined, resulting in also a closed multiplication structure (ℋ′(R), .). In this paper, the general multiplication product formula for this structure is derived. Multiplication of AHDs on R is associative, except for critical triple products. These critical products are shown to be non-associative in a simple and interesting way. The non-associativity is necessary and sufficient to circumvent Schwartz's impossibility theorem on the multiplication of distributions. | |
| dc.language | eng | |
| dc.title | Multiplication product formula for associated homogeneous distributions on R | |
| dc.type | Article | |
| dc.subject.frascati | Mathematics | |
| dc.audience | Scientific | |
| dc.subject.free | Convolution structure | |
| dc.subject.free | Convolution theorems | |
| dc.subject.free | Generalized functions | |
| dc.subject.free | Homogeneous distribution | |
| dc.subject.free | multiplication | |
| dc.subject.free | Real line | |
| dc.subject.free | Convolution | |
| dc.source.title | Mathematical Methods in the Applied Sciences | |
| dc.source.volume | 34 | |
| dc.source.issue | 12 | |
| dc.source.page | 1460-1471 | |
| Orfeo.peerreviewed | Yes | |
| dc.identifier.doi | 10.1002/mma.1455 | |
| dc.identifier.scopus | 2-s2.0-79960831438 |
