On a new positive extension problem for block Toeplitz matrices

Daniel Alpay; Vladimir Bolotnikov; Philippe Loubaton

doi:10.1016/S0024-3795(97)00048-7

On a new positive extension problem for block Toeplitz matrices

Daniel Alpay
, Vladimir Bolotnikov
, Philippe Loubaton

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We consider positive extension problems for block Toeplitz matrices when the specified entries form a stalactite type pattern. These problems do not seem in general to be amenable to the classical methods (they correspond to bitangential interpolation problems in the class of Carathéodory functions of a kind usually not solvable by the classical methods of interpolation). We solve these problems by reduction to a tangential interpolation with symmetries in a Carathéodory class.

Original language	English
Pages (from-to)	247-287
Number of pages	41
Journal	Linear Algebra and Its Applications
Volume	268
Issue number	1-3
DOIs	https://doi.org/10.1016/S0024-3795(97)00048-7
State	Published - 1 Jan 1998

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/S0024-3795(97)00048-7

Cite this

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title = "On a new positive extension problem for block Toeplitz matrices",

abstract = "We consider positive extension problems for block Toeplitz matrices when the specified entries form a stalactite type pattern. These problems do not seem in general to be amenable to the classical methods (they correspond to bitangential interpolation problems in the class of Carath{\'e}odory functions of a kind usually not solvable by the classical methods of interpolation). We solve these problems by reduction to a tangential interpolation with symmetries in a Carath{\'e}odory class.",

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AU - Bolotnikov, Vladimir

AU - Loubaton, Philippe

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N2 - We consider positive extension problems for block Toeplitz matrices when the specified entries form a stalactite type pattern. These problems do not seem in general to be amenable to the classical methods (they correspond to bitangential interpolation problems in the class of Carathéodory functions of a kind usually not solvable by the classical methods of interpolation). We solve these problems by reduction to a tangential interpolation with symmetries in a Carathéodory class.

AB - We consider positive extension problems for block Toeplitz matrices when the specified entries form a stalactite type pattern. These problems do not seem in general to be amenable to the classical methods (they correspond to bitangential interpolation problems in the class of Carathéodory functions of a kind usually not solvable by the classical methods of interpolation). We solve these problems by reduction to a tangential interpolation with symmetries in a Carathéodory class.

UR - https://www.scopus.com/pages/publications/0042858619

U2 - 10.1016/S0024-3795(97)00048-7

DO - 10.1016/S0024-3795(97)00048-7

M3 - Article

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EP - 287

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

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ER -

On a new positive extension problem for block Toeplitz matrices

Abstract

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