Nevanlinna-Pick interpolation for time-varying input-output maps:
The discrete case.- 0. Introduction.- 1. Preliminaries.- 2.
J-Unitary operators on ?2.- 3. Time-varying Nevanlinna-Pick
interpolation.- 4. Solution of the time-varying tangential
Nevanlinna-Pick interpolation problem.- 5. An illustrative
example.- References.- Nevanlinna-Pick interpolation for
time-varying input-output maps: The continuous time case.- 0.
Introduction.- 1. Generalized point evaluation.- 2. Bounded
input-output maps.- 3. Residue calculus and diagonal expansion.- 4.
J-unitary and J-inner operators.- 5. Time-varying Nevanlinna-Pick
interpolation.- 6. An example.- References.- Dichotomy of systems
and invertibility of linear ordinary differential operators.- 1.
Introduction.- 2. Preliminaries.- 3. Invertibility of differential
operators on the real line.- 4. Relations between operators on the
full line and half line.- 5. Fredholm properties of differential
operators on a half line.- 6. Fredholm properties of differential
operators on a full line.- 7. Exponentially dichotomous operators.-
8. References.- Inertia theorems for block weighted shifts and
applications.- 1. Introduction.- 2. One sided block weighted
shifts.- 3. Dichotomies for left systems and two sided systems.- 4.
Two sided block weighted shifts.- 5. Asymptotic inertia.- 6.
References.- Interpolation for upper triangular operators.- 1.
Introduction.- 2. Preliminaries.- 3. Colligations &
characteristic functions.- 4. Towards interpolation.- 5. Explicit
formulas for ?.- 6. Admissibility and more on general
interpolation.- 7. Nevanlinna-Pick Interpolation.- 8.
Caratheodory-Fejer interpolation.- 9. Mixed interpolation
problems.- 10. Examples.- 11. Block Toeplitz & some
implications.- 12. Varying coordinate spaces.- 13. References.-
Minimality and realization of discrete time-varying systems.- 1.
Preliminaries.- 2. Observability and reachability.- 3. Minimality
for time-varying systems.- 4. Proofs of the minimality theorems.-
5. Realizations of infinite lower triangular matrices.- 6. The
class of systems with constant state space dimension.- 7.
Minimality and realization for periodical systems.- References.
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