Algebraic properties and applications of the h -Hartley convolution on 𝕋 h

This paper constructs the h-Hartley convolution operator on the time scale Th, h>0. From this construction, we establish some basic properties of the operator, including boundedness on the space l1, the factorization identity, and related algebraic properties. In particular, we identify the unit element of the convolution algebra. The obtained results are applied to study solvability in l1 of a Fredholm equation of the second kind and the Cauchy problem for the Schrödinger equation on Th, h>0. In addition, we provide numerical simulations for illustration.