Suppleness of some quotient spaces of microfunctions

Abstract

The theory of microfunctions which Sato introduced contributed very much to that of linear partial differential equations. He constructed a useful transformation of these equations by expanding the analytic singularities of a hyperfunction onto the cosphere bundle. We stick not only to the analytic singularities but also to some other singularities of some subclasses of hyperfunctions which Komatsu [7], Hormander [4], Eida [2] and others have introduced. For this reason, in this paper we develop the theory of some quotient spaces of microfunctions. We state the suppleness of the sheaves of these functions which is important for the theory of microdifferential equations. Our investigations enable us to introduce the notions SS* and SS1/* for hyperfunctions. © 2000 Rocky Mountain Mathematics Consortium.