Estimates for certain integrals of products of six Bessel functions

TL;DR

This paper provides numerical estimates for integrals involving sixfold products of Bessel functions, using elementary methods, with applications to Fourier restriction inequalities on the circle.

Contribution

It introduces new numerical estimation techniques for complex Bessel function integrals relevant to Fourier analysis.

Findings

Established accurate numerical bounds for integrals of six Bessel functions

Demonstrated the applicability of elementary methods in complex integral estimation

Contributed to the understanding of Fourier restriction inequalities

Abstract

We establish good numerical estimates for a certain class of integrals involving sixfold products of Bessel functions. We use relatively elementary methods. The estimates will be used in the study of a sharp Fourier restriction inequality on the circle.