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Sheaves of quaternionic hyperfunctions and microfunctions. (English) Zbl 0819.30030
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 Cauchy-Kovalevskaya product. Finally a sheaf of quaternionic microfunctions is introduced as the microlocalization of $$F$$, and its main properties are studied.
Reviewer: A.Fabiano

##### MSC:
 30G35 Functions of hypercomplex variables and generalized variables 46F15 Hyperfunctions, analytic functionals
##### Keywords:
quaternionic hyperfunctions
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