Positivity of oscillatory integrals and Hankel transforms

In consideration of the integral transform whose kernel arises as an oscillatory solution of certain second-order linear differential equation, its positivity is investigated on the basis of Sturm's theory. As applications, positivity criteria are obtained for Hankel transforms as well as trigonometric integrals defined on the positive real line.

Automated summary

This article investigates the positivity of an integral transform by using Sturm's theory, where the kernel of the transform arises from an oscillatory solution of a second-order linear differential equation. Positivity criteria for Hankel transforms and trigonometric integrals defined on the positive real line are obtained as applications.