The reduced operators of singularly perturbed Wiener–Hopf matrices

Abstract

The reduced problem is formulated for singularly perturbed pseudodifferential equations with unknown potentials and with general boundary conditions. Several classes of problems of this type have previously been investigated in [2,5,6,7]. The stability theory [5,7] and the asymptotic analysis [6,7] for coercive singularly perturbed problems without potentials is extended to the above class of problems. Systems of singular integral equations on the half line were investigated in [8], using Wiener–Hopf factorization. Wiener–Hopf matrix operators without small parameter have been introduced and investigated in [10,12].