A duality theorem for the infinite hartley transform

This paper gives a new property for the Infinite Hartley Transform known as the Duality Theorem. The Infinite Hartley Transform is an integral transform and is closely reminiscent to the famous Infinite Fourier Transform. Unlike the former, the latter has not been much renowned in the mathematical world or its applications' domain. Most of the properties of the Infinite Hartley Transform and the Infinite Fourier Transform are quite similar but some differences do persist. A derivation of the Duality Theorem corresponding to Infinite Hartley Transform is presented. The utility of Duality Theorem lies in computing the continuous time-domain function from the Hartley frequency domain and vice versa. This has the tenacity to recede sufficient labour involved in integration. This in turn leads in the saving of precious computation time and implementation cost to a maximum limit. This Duality Theorem can be used in diverse fields such as Signal Processing, Image Processing, and Communication Systems, where it is common to encounter cases involving the continuous - time and the continuous frequency signals to have the same aspect or resemblance.