This preprint was accepted December 26, 2004
ABSTRACT: In [1], D.~Clark considered certain families of positive singular measures on the unit circle associated to inner functions $\theta$ in the unit disk. These measures were shown to be the spectral measures of unitary rank-one perturbations of the model operator acting on the (scalar) model space $K_\theta$, a subspace of the Hardy space $H^2$. In particular, it was shown that $K_\theta$ can be mapped unitarily onto $L^2(\sigma)$ for any of such measures $\sigma$. Later it was proved [2] that this mapping, which could be viewed as a generalization of the classical Fourier transform, actually takes functions from $K_\theta$ to their angular boundary values, which exist $\sigma$@-almost everywhere for any such $\sigma$. In this paper we present an analog of the above-mentioned results for vector-valued model spaces. [Full text: (.ps.gz)]
Back to all preprints
Back to the Steklov Institute of Mathematics at St.Petersburg