Non Oscillatory Functions and A Fourier Inversion Theorem for Some Functions of Very Moderate Decrease

TL;DR

This paper proves a Fourier Inversion Theorem for non oscillatory functions with moderate decrease, using nonstandard analysis techniques to establish the result.

Contribution

It introduces a Fourier Inversion Theorem applicable to a new class of functions characterized by very moderate decrease, expanding the scope of Fourier analysis.

Findings

Established Fourier Inversion for non oscillatory functions

Utilized nonstandard analysis methods in proofs

Extended Fourier analysis to functions with moderate decrease

Abstract

We consider non oscillatory functions and prove an everywhere Fourier Inversion Theorem for functions of very moderate decrease. The proofs rely on some ideas in nonstandard analysis.