An Addendum to the Multiplication and Factorization Theorems of Brodskiĭ-Livšic-Potapov

Seppo Hassi; Henk de Snoo; Eduard Tsekanovskii

An Addendum to the Multiplication and Factorization Theorems of Brodskiĭ-Livšic-Potapov

Seppo Hassi, Henk de Snoo, Eduard Tsekanovskii

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In this paper the classical Brodskiĭ-Livšic operator colligation is generalised to certain pairs of bounded linear operators and the corresponding characteristic operator-valued (transfer) function is introduced. The fundamental results due to M.S. Brodskiĭ, M.S. Livšic, and V.P. Potapov are then extended to such colligations. These new types of colligations can be used to obtain, for instance, realization results for general Herglotz-Nevanlinna functions.

Originele taal-2	English
Pagina's (van-tot)	125-133
Aantal pagina's	8
Tijdschrift	Applicable Analysis
Volume	77
Nummer van het tijdschrift	1-2
Status	Published - 2001

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title = "An Addendum to the Multiplication and Factorization Theorems of Brodskiĭ-Liv{\v s}ic-Potapov",

abstract = "In this paper the classical Brodskiĭ-Liv{\v s}ic operator colligation is generalised to certain pairs of bounded linear operators and the corresponding characteristic operator-valued (transfer) function is introduced. The fundamental results due to M.S. Brodskiĭ, M.S. Liv{\v s}ic, and V.P. Potapov are then extended to such colligations. These new types of colligations can be used to obtain, for instance, realization results for general Herglotz-Nevanlinna functions.",

keywords = "multiplication and factorization of colligations, characteristic (transfer) function, operator colligation",

author = "Seppo Hassi and Snoo, {Henk de} and Eduard Tsekanovskii",

note = "Relation: http://www.rug.nl/informatica/organisatie/overorganisatie/iwi Rights: University of Groningen, Research Institute for Mathematics and Computing Science (IWI)",

year = "2001",

language = "English",

volume = "77",

pages = "125--133",

journal = "Applicable Analysis",

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T1 - An Addendum to the Multiplication and Factorization Theorems of Brodskiĭ-Livšic-Potapov

AU - Hassi, Seppo

AU - Snoo, Henk de

AU - Tsekanovskii, Eduard

N1 - Relation: http://www.rug.nl/informatica/organisatie/overorganisatie/iwi Rights: University of Groningen, Research Institute for Mathematics and Computing Science (IWI)

PY - 2001

Y1 - 2001

N2 - In this paper the classical Brodskiĭ-Livšic operator colligation is generalised to certain pairs of bounded linear operators and the corresponding characteristic operator-valued (transfer) function is introduced. The fundamental results due to M.S. Brodskiĭ, M.S. Livšic, and V.P. Potapov are then extended to such colligations. These new types of colligations can be used to obtain, for instance, realization results for general Herglotz-Nevanlinna functions.

AB - In this paper the classical Brodskiĭ-Livšic operator colligation is generalised to certain pairs of bounded linear operators and the corresponding characteristic operator-valued (transfer) function is introduced. The fundamental results due to M.S. Brodskiĭ, M.S. Livšic, and V.P. Potapov are then extended to such colligations. These new types of colligations can be used to obtain, for instance, realization results for general Herglotz-Nevanlinna functions.

KW - multiplication and factorization of colligations

KW - characteristic (transfer) function

KW - operator colligation

M3 - Article

SN - 0003-6811

VL - 77

SP - 125

EP - 133

JO - Applicable Analysis

JF - Applicable Analysis

IS - 1-2

ER -

An Addendum to the Multiplication and Factorization Theorems of Brodskiĭ-Livšic-Potapov

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