Summary: We investigate systems of linear integral equations in the space of -vector valued functions which are regulated on the closed interval (i.e. such that can have only discontinuities of the first kind in ) and left-continuous in the corresponding open interval In particular, we are interested in systems of the form
where , the columns of the -matrix valued function belong to , the entries of have a bounded variation on for any and the mapping is regulated on and left-continuous on as the mapping with values in the space of -matrix valued functions of bounded variation on The integral stands for the Perron-Stieltjes one treated as the special case of the Kurzweil-Henstock integral.
In particular, we prove basic existence and uniqueness results for the given equation and obtain the explicit form of its adjoint equation. A special attention is paid to the Volterra (causal) type case. It is shown that in that case the given equation possesses a unique solution for any right-hand side from , and its representation by means of resolvent operators is given.