On the decomposition of Schwartz function and its applications

Abstract

In this paper, we use the constructive methods to show that every Schwartz function can be decom-posed as a product of two Schwartz functions. The same is true for D (R n ) function with the same compact set. As their applications, it immediately follows that g (R n )= g (R n ) g (R n ) and D (R n )= D (R n ) D (R n ). It should be pointed out that we use the adaptive idea and method to give the decompositions.