Products of Distributions in Colombeau Algebra

Miteva, Marija (2019) Products of Distributions in Colombeau Algebra. In: Kongres mladih matematicara u Novom Sadu.

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Abstract

The problem about product of two arbitrary distributions is one of the main problems that classical theory of distributions had came across. Many attempts have been done for overcoming this problem. The construction of the Colombeau algebra seems to be an optimal solution until now for dealing with products of distributions. Colombeau algebra is an associative, differential algebra and
the space of Schwartz distributions is embedded in it. The most important feature of the Colombeau algebra is that the product of elements in it generalises the classical product of distributions, thus the classical product of two distributions, if it exists, and the new one obtained in Colombeau algebra (Colombeau product of distributions) are equal. Furthermore, in Colombeau algebra we can
obtain many products of two singular distributions which in the classical theory are not defined. One of the advantages of Colombeau theory of generalized functions is that we can operate with singular distributions easily as well as with smooth functions.
I will present the idea for the construction of such algebra and some examples with results about products of two singular distributions that can not be calculated in the classical theory of distributions.

Item Type:	Conference or Workshop Item (Paper)
Subjects:	Natural sciences > Matematics
Divisions:	Faculty of Computer Science
Depositing User:	Marija Miteva
Date Deposited:	02 Feb 2023 09:31
Last Modified:	02 Feb 2023 09:31
URI:	https://eprints.ugd.edu.mk/id/eprint/31205

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