Fundamental properties of modified Fourier hyperfunctions (Q1079154)

There are three types of (vector-valued) Fourier hyperfunctions: classical (1960, 1975), modified (1976) and of mixed type (1981). The sheaves of these three types of Fourier hyperfunctions are defined on \(D^ n\), the radial compactification of \(R^ n\), all three of them are flabby, and each space of global sections of sheaves is stable under Fourier transformation. The difference between them lies essentially in the domains of the defining functions. In this paper complete proofs are given of the theorems on the fundamental properties of the sheaf \({\mathcal R}\) of modified Fourier hyperfunctions of \(D^ n\), a.o. the glabbiness of \({\mathcal R}\), the duality between \({\mathcal R}\) and the space of rapidly decreasing real analytic functions of \(D^ n\), and the Fourier transform of the modified Fourier hyperfunctions.