Article

GSTF Journal of Mathematics, Statistics and Operations Research (JMSOR)

, 3:2

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

New Algebra of New Generalized Functions

  • Ramadan SabraAffiliated withJazan University

Abstract

In 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 EE* ⊂ 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 .

Keywords

Localy convex algebra distribution algebra