Sheaves of quaternionic hyperfunctions and microfunctions

Abstract

The sheaf F - of quaternionic hyperfunctions is introduced as the sheaf of boundary values of quaternionic regular functions. A Köthe duality type theorem is established to prove the isomorphism between compactly supported quaternionic hyperfunctions and compactly supported regular functionals. Ordinary differential operators are studied on the sheaf F with the use of the C ? K product. Finally a sheaf of quaternionic microfunctions is introduced as the microlocalization of F , and its main properties are studied.