A quantitative Riemann-Lebesgue lemma with application to equations with memory

TL;DR

This paper provides a quantitative version of the Riemann-Lebesgue lemma for functions on the half line and applies it to differential equations with memory effects.

Contribution

It introduces an elementary proof of a quantitative Riemann-Lebesgue lemma and demonstrates its application to models with memory.

Findings

Established a quantitative Riemann-Lebesgue lemma for half-line functions

Applied the lemma to analyze differential equations with memory

Provided insights into the decay properties of solutions

Abstract

An elementary proof of a quantitative version of the Riemann-Lebesgue lemma for functions supported on the half line is given. Applications to differential models with memory are discussed.