Boundary convergence of vector-valued pseudocontinuable functions

摘要

In the first part of the paper we discuss a multi-dimensional analogue of the well-known construction by D. Clark that allows one to study families of spectral measures of perturbations of the model contraction. In the second part we present extensions of the relevant results on the boundary behavior of pseudocontinuable functions. We show that, although the most direct analogue of the scalar theorem on the existence of boundary values for pseudocontinuable functions with respect to Clark measures fails in the non-scalar situation, suitable vector-valued versions of such results can be found. (C) 2006 Elsevier Inc. All rights reserved.