Title

The Fourier transform of thick distributions

Document Type

Article

Publication Date

7-1-2021

Abstract

We first construct a space (cn) whose elements are test functions defined in cn = n {∞}, the one point compactification of n, that have a thick expansion at infinity of special logarithmic type, and its dual space ′(cn), the space of sl-thick distributions. We show that there is a canonical projection of ′(cn) onto ′(n). We study several sl-thick distributions and consider operations in ′(cn). We define and study the Fourier transform of thick test functions of (n) and thick tempered distributions of ′(n). We construct isomorphisms : ′(n) →′(cn), : ′(cn) → ′(n), that extend the Fourier transform of tempered distributions, namely, = and =, where are the canonical projections of ′(n) or ′(cn) onto ′(n). We determine the Fourier transform of several finite part regularizations and of general thick delta functions.

Publication Source (Journal or Book title)

Analysis and Applications

First Page

621

Last Page

646

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