Multiplication of Distributions and Algebras of Mnemofunctions

In this paper, we discuss methods and approaches for definition of multiplication distributions, which is not defined in general the classical theory. We show that problem related to fact operator by a smooth function nonclosable space distributions. give method construction new objects called or mnemofunctions, preserve essential properties usual distributions produce algebras as well. describe various embedding distribution spaces into mnemofunctions. All ideas considerations are illustrated simplest example on circle. Some effects arising study equations with coefficients demonstrated linear first-order differential equation.