New Algebra of New Generalized Functions

Abstract

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