ON THE CONVOLUTION EQUATION RELATED TO THE LAPLACE OPERATOR

In this article, we study the distribution for ,where is the partial differential operator related to Laplace operator iterated times, is the Dirac delta distribution, is a variable in , and ) is a constant. In particular, we study the application of for solving the solution of some convolution equation. We find that the types of solutions to such convolution equations, such as the ordinary function and the singular distribution, depend on the relationship between and