Convolution theorems associated with quaternion linear canonical transform and applications

Novel types of convolution operators for quaternion linear canonical transform (QLCT) are proposed. Type one and two defined in the spatial QLCT spectral domains, respectively. They distinct space consistent once complex or real space. Various formulas discussed. Consequently, quaternionic functions can be implemented by product their QLCTs, summation products QLCTs. As applications, correlation theorems derived. The proposed used to solve Fredholm integral equations with special kernels. Some systems second-order partial differential equations, which transformed into solved as well. a final point, we demonstrate that theorem facilitates design multiplicative filters.