Preface vi i
Part I . Engineerin g motivatio n
1. Engineerin g backgroun d 3
What i s the transfe r function—ho w analyti c function s aris e in
engineering-connection laws.
2. Engineerin g problem s 11
Engineering problems (vs . analysis); a control paradigm.
Part II . Analyti c functio n theor y
How much classical analysi s can you get by staring a t pair s of
invariant subspaces ? Ther e i s a unifie d wa y o f obtainin g th e
theories of classical interpolation , H°° approximation , Coron a
= Bezou t identities , commutant lifting , Wiener-Hop f factoriza -
tion, integrabl e system s (Tod a Lattice , KdV) , matri x L U de-
compositions, interpolation , uppe r triangula r approximation .
The method give s excellent result s when al l functions induce d
are differentiable an d in these cases frequently extend s existing
results i n variou s ways , e.g. , treat s adde d symmetries , allow s
poles in H°° functions .
3. Fractiona l map s an d Grassmannian s 2 1
Basic projective lore. Th e correspondences between linear frac-
tional actions on operators and linear actions on subspaces.
4. Representin g shif t invarian t subspace s 3 5
5. Application s t o factorization , interpolation , an d
approximation 4 3
6. Furthe r application s 5 7
7. Matri x analog s an d generalization s 7 3
A general theor y whic h contains bot h th e matrix an d analyti c
function case .
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