###
Steklov Institute of Mathematics at St.Petersburg

#
PREPRINT 23/2004

Vladimir Kapustin and Alexei Poltoratski ##
BOUNDARY BEHAVIOR IN VECTOR-VALUED
STAR-INVARIANT SUBSPACES

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