On spectral factorization and geometric control.
The characterization of all the minimum
degree spectral factors $W$ of a given $p \times
p$ spectral density $\Phi$ of rank $m_0$ is a
problem which has been widely studied in
connection with the lattice of
symmetric solutions to the Riccati inequality
associated to $\Phi$. But the differential
structure of the set of minimal spectral
factors of a given dimension is not well
known. Moreover there are important
connections with the geometric control theory
of Wonham which have only been investigated
recently (by Lindquist, Michaletzky and Picci).
We show much stronger results which connect
$(A,B)$-invariant subspaces to projections of
coinvariant subspaces on the state space. The
motivation for this study stems from a
simple formulation of an econometric
problem (dynamic Frisch scheme) for which we
will give an example. The work is
done in cooperation partly with L.Baratchart and
partly with P.A. Fuhrmann.
Dr Andrea Gombani (LADSEB-CNR, Padova)