Algorithme de Schur: espaces a noyau reproduisant et theorie des systemes

The same positive functions (in the sense of reproducing kernel spaces) appear
in a natural way in two different domains, namely the modeling of time-invariant
dissipative linear systems and the theory of linear operators. We use the associated
reproducing kernel Hilbert spaces to study the relationships between these domains. The inverse scattering problem plays a key role in the exposition. The reproducing kernel approach allows to tackle in a natural way more general cases, such as nonstationary systems, the case of non positive metric and the case of pairs of commuting nonself-adjoint operators.