where γj are selfadjoint 4× 4matrices satisfying the relations (2) γjγl + γlγj = 2δl,j . Obviously, if the domain of D0 is defined asH1(R3;C4), then D0 is a selfadjoint operator in L2(R3;C4). The spectrum of D0 is absolutely continuous, it coincides with the complement of the interval (−1, 1) as a set: σ(D0) = σa.c.(D0) = (−∞,−1] ∪ [1,∞). The multiplicity of the spectrum is infinite. We see tha...

In this paper we prove the existence and the uniqueness of the solutions of the Hammerstein-Volterra integral equation in the space of the absolutely continuous functions endowed with the bounded variation norm. After that, we find the resolvent of the corresponding linear integral equation in order to obtain a variation of parameters formula for the solutions of this linear equation. Finally, ...