Integral geometry and valuation theory form a dynamic field at the intersection of geometric analysis and algebraic topology. This discipline addresses the study of measures – known as valuations – ...

Main goal of this paper is to establish various basic formulas for the generalized integral transform involving the generalized convolution product. In order to establish these formulas, we use the ...

The study of Hilbert transforms and oscillatory integrals has long been a focal point in harmonic analysis, embedding profound implications across pure and applied mathematics. The Hilbert transform, ...

The definite integral $M(a)\coloneq \frac{4}{\pi}\int_{0}^{\pi /2}\frac{x^{2}dx}{x^{2}+\text{ln}^{2}(2e^{-a}\text{cos}x)}$ is related to the Laplace transform of the ...

This alternative technique is applied in areas such as optics and engineering, as well as in financial derivatives pricing. It allows complex integrals to be evaluated straightforwardly when other ...