Factorization of Hilbert port operators with poles on the imaginary axis. (English) Zbl 0627.47008
In classical network theory scattering, chain and transfer operators corresponding to passive n-ports are meromorphic matrix functions, J- expansive in the right half plane Re p\(>0\), which satisfy the reality condition \(S(\bar p)=\overline{S(p)}.\)
The author’s abstract: A factorization method is given to extract poles located on the imaginary axis for J-biexpansive meromorphic operator- valued functions acting on an infinite-dimensional Hilbert space. Decomposition of a real operator in terms of real factors, applicable to Hilbert ports, is also described, thus generalizing synthesis techniques originally developed for passive n-ports.
The author’s abstract: A factorization method is given to extract poles located on the imaginary axis for J-biexpansive meromorphic operator- valued functions acting on an infinite-dimensional Hilbert space. Decomposition of a real operator in terms of real factors, applicable to Hilbert ports, is also described, thus generalizing synthesis techniques originally developed for passive n-ports.
Reviewer: T.Nakazi
MSC:
| 47A68 | Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators |
| 47A56 | Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) |
| 47A40 | Scattering theory of linear operators |
Keywords:
network theory scattering; chain and transfer operators; J-biexpansive meromorphic operator-valued functions acting on an infinite-dimensional Hilbert space; Decomposition of a real operator in terms of real factors; synthesis techniques; passive n-portsReferences:
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