Algebra of mnemofunctions on a circle

It is impossible to define the product of arbitrary generalized functions in the classical theory of distributions. That is an obstacle for applications generalized functions theory to equations with generalized coefficients and nonlinear problems. The common approach for solving the problem of generalized functions multiplication consists in constructing a differential algebra $G$ according to the given space of generalized functions $E$ and building an embedding $R: E\to G$ Such algebras $G$ are called Colombeau type algebras and their elements are called new generalized functions or mnemofunctions. The algebra of mnemofunctions on the circle is constructed in this article. By this example some general questions on algebras of mnemofunctions are formulated.