The geometry of Darlington synthesis (in memory of W. Cauer)

Patrick Dewilde

Displaying similar documents to “The geometry of Darlington synthesis (in memory of W. Cauer)”

Generalizations of Hankel operators

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Linear prediction: Mathematics and engineering.

Bultheel, Adhemar, Van Barel, Marc (1994)

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Sz. Nagy-Foias theory and similarity for a class of Toeplitz operators

Douglas Clark (1982)

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The Szegö and Beurling theorems and operator factorizations

Lavon Page (1982)

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Hankel forms and the Fock space.

Svante Janson, Jaak Peetre, Richard Rochberg (1987)

Revista Matemática Iberoamericana

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Reproducing kernels and Riccati equations

Harry Dym (2001)

International Journal of Applied Mathematics and Computer Science

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The purpose of this paper is to exhibit a connection between the Hermitian solutions of matrix Riccati equations and a class of finite dimensional reproducing kernel Krein spaces. This connection is then exploited to obtain minimal factorizations of rational matrix valued functions that are J-unitary on the imaginary axis in a natural way.

On Pták’s generalization of Hankel operators

Carmen H. Mancera, Pedro José Paúl (2001)

Czechoslovak Mathematical Journal

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In 1997 Pták defined generalized Hankel operators as follows: Given two contractions $T_{1} \in ℬ (ℋ_{1})$ and $T_{2} \in ℬ (ℋ_{2})$ , an operator $X ℋ_{1} \to ℋ_{2}$ is said to be a generalized Hankel operator if $T_{2} X = X T_{1}^{*}$ and $X$ satisfies a boundedness condition that depends on the unitary parts of the minimal isometric dilations of $T_{1}$ and $T_{2}$ . This approach, call it (P), contrasts with a previous one developed by Pták and Vrbová in 1988, call it (PV), based on the existence of a previously defined generalized Toeplitz operator. There seemed to be a strong...