The <i>h</i> -Hartley-cosine discrete generalized convolution on the time scale 𝕋 _<i>h</i>

In this article, we study the h-Hartley, h-sine, h-cosine transforms on the time scale Th, and construct the discrete generalized convolution operators for h- Hartley-cosine transform on the time scale Th. We prove Plancherel type theorem, Titchmarsh type theorem, Parseval equalities for the h-Hartley transform and discrete generalized convolutions on the time scale Th. As applications we solve Toeplitz plus Hankel type equations and systems of equations on time scale Th.