J-unitary operators and their siblings, symplectic operators, play an important role in physics and mathematics. Aside from the fact that they describe a physically interesting situation, they are instrumental in interpolation and approximation theory as well. The physical motivation is found in lossless scattering theory, which gives an operator description of wave propagation and reflection. An introduction to this is given in section 8.1. We saw in the previous chapters that reachability and observability spaces are instrumental in the realization theory of operators in general. In the case of J-unitary operators these spaces turn out to be rather special, with interesting geometrical properties (sections 8.2 and 8.4).
KeywordsState Space State Transformation Signature Matrix Hankel Operator Krein Space
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