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Realization theory for Herglotz--Nevanlinna and Schur class functions: from one to several variables and beyond Vinnikov, Victor
Description
In this survey talk I will recall how the familiar integral representation for Herglotz--Nevanlinna functions can be recast in operator theoretic or rather system theoretic terms, namely as a realization of the function as the transfer function of an input/state/output linear system. There are similar results for Schur functions, i.e., functions taking values in the unit disc (as opposed to the upper or the right halfplane). After discussing the one variable case, I will move to the case of several complex variables. It turns out that there is a very good generalization of the classical realization theory provided one considers possibly more restricted classes of functions. These classes are defined by testing the values of the function not merely on tuples of scalars but on tuples of commuting matrices of all sizes. Time permitting I will wrap up with the most recent incarnation of these ideas, where one tests the values on tuples of not necessarily commuting matrices.
Item Metadata
Title |
Realization theory for Herglotz--Nevanlinna and Schur class functions: from one to several variables and beyond
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2019-10-09T09:03
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Description |
In this survey talk I will recall how the familiar integral representation for Herglotz--Nevanlinna functions can be recast in operator theoretic or rather system theoretic terms, namely as a realization of the function as the transfer function of an input/state/output linear system. There are similar results for Schur functions, i.e., functions taking values in the unit disc (as opposed to the upper or the right halfplane). After discussing the one variable case, I will move to the case of several complex variables. It turns out that there is a very good generalization of the classical realization theory provided one considers possibly more restricted classes of functions. These classes are defined by testing the values of the function not merely on tuples of scalars but on tuples of commuting matrices of all sizes. Time permitting I will wrap up with the most recent incarnation of these ideas, where one tests the values on tuples of not necessarily commuting matrices.
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Extent |
71.0 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Ben Gurion University of the Negev
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Series | |
Date Available |
2020-04-07
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0389763
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International