On some properties of systems of Volterra integral equations of the fourth kind with kernel of convolution type (Q881063)

The author discusses existence and uniqueness of the solutions of the integral equation \[ Ax(t)+\int_{\alpha}^t K(t-s)x(s) ds = \psi(t), \;t \in [\alpha,\beta] \] with respect to the vector-function \(x(t)\). Here, \(A\) is a constant matrix, \(K(t)\) is a smooth matrix kernel. A left regularity operator is introduced and its existence is discussed for the analytic matrix-function \(K(t)\).