期刊
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS
卷 35, 期 1, 页码 61-76出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/10652469.2023.2272212
关键词
Bessel functions; Fourier transforms; Hankel transforms; oscillatory; positivity; Sturm's oscillation theory
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.
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.
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