51 research outputs found
Weighted Hardy spaces: shift invariant and coinvariant subspaces, linear systems and operator model theory
The Sz.-Nagy--Foias model theory for contraction operators
combined with the Beurling-Lax theorem establishes a correspondence between any
two of four kinds of objects: shift-invariant subspaces, operator-valued inner
functions, conservative discrete-time input/state/output linear systems, and
Hilbert-space contraction operators. We discuss an analogue of
all these ideas in the context of weighted Hardy spaces over the unit disk and
an associated class of hypercontraction operators
Prediction theory for stationary functional time series
We survey aspects of prediction theory in infinitely many dimensions, with a view to the theory and applications of functional time series
Operator theory and function theory in Drury-Arveson space and its quotients
The Drury-Arveson space , also known as symmetric Fock space or the
-shift space, is a Hilbert function space that has a natural -tuple of
operators acting on it, which gives it the structure of a Hilbert module. This
survey aims to introduce the Drury-Arveson space, to give a panoramic view of
the main operator theoretic and function theoretic aspects of this space, and
to describe the universal role that it plays in multivariable operator theory
and in Pick interpolation theory.Comment: Final version (to appear in Handbook of Operator Theory); 42 page
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