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arXiv · 1401.3143

New inversion, convolution and Titchmarsh's theorems for the half-Hartley transform

Semyon Yakubovich
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Abstract

The generalized Parseval equality for the Mellin transform is employed to prove the inversion theorem in L_2 with the respective inverse operator related to the Hartley transform on the nonnegative half-axis (the half-Hartley transform). Moreover, involving the convolution method, which is based on the double Mellin-Barnes integrals, the corresponding convolution and Titchmarsh's theorems for the half-Hartley transform are established. As an application, we consider solvability conditions for a homogeneous integral equation of the second kind involving the Hartley kernel.

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Semyon Yakubovich. 2014-03-10. New inversion, convolution and Titchmarsh's theorems for the half-Hartley transform. https://arxiv.org/abs/1401.3143

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