Geodesic
Multiplication of distributions and algebras of mnemofunctions
Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 65 (2019) no. 3, pp. 339-389

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we discuss methods and approaches for definition of multiplication of distributions, which is not defined in general in the classical theory. We show that this problem is related to the fact that the operator of multiplication by a smooth function is nonclosable in the space of distributions. We give the general method of construction of new objects called new distributions, or mnemofunctions, that preserve essential properties of usual distributions and produce algebras as well. We describe various methods of embedding of distribution spaces into algebras of mnemofunctions. All ideas and considerations are illustrated by the simplest example of the distribution space on a circle. Some effects arising in study of equations with distributions as coefficients are demonstrated by example of a linear first-order differential equation. 
@article{CMFD_2019_65_3_a0,
     author = {A. B. Antonevich and T. G. Shahava},
     title = {Multiplication of distributions and algebras of mnemofunctions},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {339--389},
     publisher = {mathdoc},
     volume = {65},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2019_65_3_a0/}
}
TY  - JOUR
AU  - A. B. Antonevich
AU  - T. G. Shahava
TI  - Multiplication of distributions and algebras of mnemofunctions
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2019
SP  - 339
EP  - 389
VL  - 65
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMFD_2019_65_3_a0/
LA  - ru
ID  - CMFD_2019_65_3_a0
ER  - 
%0 Journal Article
%A A. B. Antonevich
%A T. G. Shahava
%T Multiplication of distributions and algebras of mnemofunctions
%J Contemporary Mathematics. Fundamental Directions
%D 2019
%P 339-389
%V 65
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMFD_2019_65_3_a0/
%G ru
%F CMFD_2019_65_3_a0
A. B. Antonevich; T. G. Shahava. Multiplication of distributions and algebras of mnemofunctions. Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 65 (2019) no. 3, pp. 339-389. http://geodesic.mathdoc.fr/item/CMFD_2019_65_3_a0/