A Fourier transform and convolution of Diamond operator

In this paper, we define a new operator and give a sense of distribution theory to find the Fourier transform of new operator. It was found that the Fourier transform of new operator related to the Fourier transform of ultrahyperbolic operator and Diamond operator. And we also study the convolution products \(\Box^{k}\delta \ast \Box^{l}\) and \(\diamondsuit^{k}\delta\ast \diamondsuit^{l}.\)