Association between temperate distributions and analytical functions in the context of wave-front sets

摘要

Let ß be a translation invariant Banach function space (BF-space). In this paper we prove that every temperate distribution f can be associated with a function F analytic in the convex tube Ω — {z ∈ C~d; | Im z| < 1} such that the wave-front set of / of Fourier BF-space types in intersection with R~d × S~(d-1) consists of the points (x, ξ) such that F does not belong to the Fourier BF-space at x — iξ.