Miteva, Marija and Koceva Lazarova, Limonka (2024) Application of Algebras in Evaluating Products of Distributions. In: Computer Science and Mathematics, 21-23 May, 2024, Ohrid, Republic of North Macedonia. (Unpublished)
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Abstract
The classical theory of Schwartz distributions is concerned with a problem of multiplication of distributions, because the product of two arbitrary singular distributions is not defined in it. Looking for a solution of this problem, the Co-lombeau Algebra of generalized functions was constructed. The properties of the Colombeau algebra allow us to evaluate products of singular distribu-tions which are not defined in the Schwartz classical theory. A notion of ‘as-sociation’ in Colombeau algebra is introduced in order to allow us obtained results to be consider as products in the classical theory of distributions. Thus, according to the properties of Colombeau algebra, we can evaluate products of distributions which are not defined in the Schwartz theory. The definition of the product of distributions in Colombeau algebra can be con-sidered as generalization of their classical product in Schwartz theory.
| Item Type: | Conference or Workshop Item (Speech) |
|---|---|
| Subjects: | Natural sciences > Matematics |
| Divisions: | Faculty of Computer Science |
| Depositing User: | Marija Miteva |
| Date Deposited: | 01 Oct 2024 08:15 |
| Last Modified: | 01 Oct 2024 08:15 |
| URI: | https://eprints.ugd.edu.mk/id/eprint/34729 |
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