On Some Properties of Systems of Volterra Integral Equations of the Fourth Kind with Kernel of Convolution Type

We consider the system of integral equations of the form $Ax+Vx=\nobreak \psi$, where $V$ is the Volterra operator with kernel of convolution type and $A$ is a constant matrix, $\det A=\nobreak 0$. We prove an existence theorem and establish necessary and sufficient conditions for the kernel of the operator of the system to be trivial.