S-Bounded distributions, application to partial differential equations

Abstract

The S-boundness at infinity of a distribution is defined to give some informations on the behaviour of a large class of distributions at infinity. The subspace A′ ⊆ D′ of S-bounded distributions has been characterized and the properties of elements of A′ have been analyzed especially those interesting for partial differential equations. At the end, some propositions, concerning the S-boundness of solutions of linear partial differential equations have been proved.

Keywords:

• Distributions
• S-boundedness
• locally convex topological vector spaces

AMS:

• 46F10
• 35B40