We prove that if(A,μ) generate an exponentially bounded k-convoluted solution operator families,then(AB,μ),(BA,μ) or(A(I+B),μ),((I+B)A,μ) also generate an exponentially bounded k-convoluted solution operator families.

We present a new method for designing kernel function of H~n(R) using kernel function of H~1(R) and convolution operator.

A new good method for computing the reproducing kernels of H″(R) (n ∈Z + and n ≠1) presented was based on the use of the reproducing kernel of H 1(R) and the convolution operator in this paper.

Ehrenpreis and Hormander discussed the solvability of convolution operators in Schwartz space.

Using results of the representations of two_step nilpotent groups and convolution operators, the paper discusses the relation between the convolution operators and the pseudodifferential operators.

Using the general theory of the unitary representations of nilpotent groups and the formulas of unitary representations of two_step nilpotent groups,we obtain the concrete representation of the distributions and convolution operators on two_step nilpotent Lie groups.

Using convolution operators this paper discusses the solution of convolution-type Volterra integral equations by means of operators, and a new algorithm of solving kernel is obtained.