Fabiano, Adelina; Gentili, Graziano; Struppa, Daniele C. Sheaves of quaternionic hyperfunctions and microfunctions. (English) Zbl 0819.30030 Complex Variables, Theory Appl. 24, No. 3-4, 161-184 (1994). 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 Cited in 2 ReviewsCited in 9 Documents MSC: 30G35 Functions of hypercomplex variables and generalized variables 46F15 Hyperfunctions, analytic functionals Keywords:quaternionic hyperfunctions PDFBibTeX XMLCite \textit{A. Fabiano} et al., Complex Variables, Theory Appl. 24, No. 3--4, 161--184 (1994; Zbl 0819.30030) Full Text: DOI