Equivalence of the Gelfand]Shilov Spaces

We prove that there is a one to one correspondence between the Gelfand]Shilov space WV of type W and the space SM MNpp of generalized type S. As an application we prove the equality W lWV M sWMV, which is a generalization of the equality SrlSssSrsfound by I. M. Gelfand and G. E. Shilov ‘‘Generalized Functions, II, III,’’ Academic Press, New YorkrLondon, 1967..