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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

30G35 Functions of hypercomplex variables and generalized variables
46F15 Hyperfunctions, analytic functionals
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