A formula for the generalized resolvent of an isometric operator for the exterior of the unit disk

In this note we establish the relationship between characteristic functions and generalized resolvents of isometric operators for the exterior of the unit disk. A certain sufficient condition is given in terms of characteristic functions that the form of the formula for the generalized resolvent be preserved across the unit circle.Translated from Matematicheskie Zametki, Vol. 13, No. 6, pp. 849–856, June, 1973.