ON THE ITERATED CONVOLUTION OPERATORS ⊛^k AND THEIR DISTRIBUTIONAL FUNDAMENTAL SOLUTIONS IN R^n

We investigate the fundamental solution of a class of higher-order differential operators defined via an iterated convolution structure, denoted by , which generalizes certain polyharmonic-type and ultra-hyperbolic operators. Within the framework of distribution theory, we construct explicit formulas for the fundamental solutions corresponding to these operators and analyze their behavior depending on the iteration order and the dimension . We also provide a classification of solutions to associated inhomogeneous equations, describing conditions under which they are classical functions, tempered distributions, or purely singular distributions. Our results offer a systematic method for solving a broad class of linear partial differential equations with constant coefficients and possess potential applications in mathematical physics and generalized function theory.