Multiplication of the distributions (x±i0)z
| dc.contributor.author | Franssens, G.R. | |
| dc.date | 2014 | |
| dc.date.accessioned | 2016-03-25T09:42:11Z | |
| dc.date.available | 2016-03-25T09:42:11Z | |
| dc.identifier.uri | https://orfeo.belnet.be/handle/internal/2854 | |
| dc.description | In previous work of the author, a convolution and multiplication product for the set of Associated Homogeneous Distributions (AHDs) with support in ℝ was defined and fully investigated. Here this definition is used to calculate the multiplication product of homogeneous distributions of the form (x±i0)z, for all z∈C. Multiplication products of AHDs generally contain an arbitrary constant if the resulting degree of homogeneity is a negative integer, i.e., if it is a critical product. However, critical products of the forms (x+i0)a.(x+i0)b and (x−i0)a.(x−i0)b, with a+b∈Z−, are exceptionally unique. This fact combined with Sokhotskii–Plemelj expressions then leads to linear dependencies of the arbitrary constants occurring in products like δ(k).δ(l), η(k).δ(l), δ(k).η(l) and η(k).η(l) for all k,l∈N (η≜1πx−1). This in turn gives a unique distribution for products like δ(k).η(l)+η(k).δ(l) and δ(k).δ(l)−η(k).η(l). The latter two products are of interest in quantum field theory and appear for instance in products of the partial derivatives of the zero-mass two-point Wightman distribution. | |
| dc.language | eng | |
| dc.title | Multiplication of the distributions (x±i0)z | |
| dc.type | Article | |
| dc.subject.frascati | Mathematics | |
| dc.audience | Scientific | |
| dc.subject.free | associated homogeneous distribution | |
| dc.subject.free | Generalized function | |
| dc.subject.free | multiplication | |
| dc.subject.free | quantum field theory | |
| dc.subject.free | Wightman distribution | |
| dc.source.title | Journal of Applied Analysis | |
| dc.source.volume | 20 | |
| dc.source.issue | 1 | |
| dc.source.page | 15-27 | |
| Orfeo.peerreviewed | Yes | |
| dc.identifier.doi | 10.1515/jaa-2014-0003 | |
| dc.identifier.scopus | 2-s2.0-84902288520 |
