  Continuous analogs of orthogonal polynomials on the circle are solutions of a
canonical system of differential equations, introduced and studied by M.G.Krein
and recently generalized to matrix systems by L.A.Sakhnovich. We prove that the
continuous analog of the adjoint polynomials converges in the upper half-plane
in the case of L^2 coefficients, but in general the limit can be defined only
up to a constant multiple even when the coefficients are in L^p for any p>2,
the spectral measure is absolutely continuous and the Szego-Kolmogorov-Krein
condition is satisfied. Thus we point out that Krein's and Sakhnovich's papers
contain an inaccuracy, which does not undermine known implications from these
results.
