Operator Theory, System Theory and Related Topics 2001
DOI: 10.1007/978-3-0348-8247-7_4
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Models of Contractions Constructed from the Defect Function of Their Characteristic Function

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Cited by 8 publications
(10 citation statements)
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“…We mention that the role of the defect functions in the theory of scattering with loss is discussed in the papers [9]- [11] and [21]. In [19] it is shown that φ θ and ψ θ are right and left semi-radii of the Weyl limit matrix ball generated by the nested sequence of Schur interpolation problems associated with θ.…”
Section: Definition 217 Let θ ∈ S(d;mentioning
confidence: 99%
See 1 more Smart Citation
“…We mention that the role of the defect functions in the theory of scattering with loss is discussed in the papers [9]- [11] and [21]. In [19] it is shown that φ θ and ψ θ are right and left semi-radii of the Weyl limit matrix ball generated by the nested sequence of Schur interpolation problems associated with θ.…”
Section: Definition 217 Let θ ∈ S(d;mentioning
confidence: 99%
“…What concerns detailed descriptions of the interrelations of these shifts and coshifts to scattering systems we refer to [9]- [11], and [21]. We note that there are close connections between representing Schur functions as block of two-sided inner functions and constructing Darlington representations of Schur functions (see Arov [1]- [5], Douglas and Helton [13]).…”
Section: Introductionmentioning
confidence: 99%
“…Clearly, if Θ(λ) is inner or co-inner, then ϕ Θ = 0 or ψ Θ = 0, respectively. The following result has been established in [26, Theorem 1.1, Corollary 1] (see also [19,Theorem 3], [20,Theorem 1.5]). where…”
Section: Moreover the Function ϕ(λ) Is Uniquely Defined Up To A Leftmentioning
confidence: 76%
“…In this expansion, the state space and the main operator will not change. The embedding of the system (1.1) is any system determined by the system operator 16) where U ′ and Y ′ are Hilbert spaces. The transfer function of the embedded system is…”
Section: Linear Systems Dilations and Embeddingsmentioning
confidence: 99%
“…ζ on the unit circle T, it holds ϕ * (ζ)ϕ(ζ) ≤ I − S * (ζ)S(ζ), and for every other operator valued analytic function ϕ with similar property, it holds ϕ * (ζ) ϕ(ζ) ≤ ϕ * (ζ)ϕ(ζ). For the existence of defect functions, see [30,Theorem V.4.2], and for a detailed treatise, see [16,17,18]. In [7], Arov et al constructed ( * -)optimal minimal passive systems in the Hilbert space setting without using defect functions.…”
Section: Introductionmentioning
confidence: 99%