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

2010/03/05 by Karoline Johansson, Johansson, Karoline
Economics, Econometrics and Finance · Mathematics · #35A18 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Stochastic processes and financial applications #math.FA #msc:35A18

paper · pdf · doi:10.48550/arxiv.1003.1281

22 pages

arxiv created 2010/03/05 · arxiv updated 2010/03/05 · openalex publication_date 2010/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let B 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 Omega=z in C^d; |Im z|<1 such that the wave-front set of f 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.

Citations

• Wave-front sets of Banach function types

Related

• Wave-front sets of Banach function types
• Tempered homogeneous function spaces, II
• Analytic functions and the Fourier transform of distributions. II
• Wave-front sets related to quasi-analytic Gevrey sequences
• Wave front sets with respect to Banach spaces of ultradistributions.\n Characterisation via the short-time Fourier transform