New Algebra of New Generalized Functions

Abstract

In this paper, we define the vector space ï(E) in which the associative multiplication is defined . Moreover we will define the embeddings of E , and * E into the algebra ï(E) , where E be a locally convex algebra , and * E the dual space of E , that is
( ) * E  E  ï E . The importance of the algebra ï(E) that we can lift operations ( linear ond bilinear ) from the space E , and * E to the algebra ï(E) , moreover we can define the multiplication of elements of * E as elements of the algebra ï(E) . Also we introduce and study the case when E S(R) the space of functions of rapid decay .