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J-Unitary Operators

In: Time-Varying Systems and Computations

Author

Listed:
  • Patrick Dewilde

    (Delft University of Technology, DIMES)

  • Alle-Jan van der Veen

    (Delft University of Technology, DIMES)

Abstract

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).

Suggested Citation

  • Patrick Dewilde & Alle-Jan van der Veen, 1998. "J-Unitary Operators," Springer Books, in: Time-Varying Systems and Computations, chapter 8, pages 191-231, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-2817-0_8
    DOI: 10.1007/978-1-4757-2817-0_8
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