Carathéodory - Fejér problem for pairs of meromorphic functions

D. Alpay; V. Bolotnikov

doi:10.1002/mana.19991990103

Carathéodory - Fejér problem for pairs of meromorphic functions

D. Alpay, V. Bolotnikov

Department of Mathematics

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Abstract

We continue our study of families of pairs of matrix - valued meromorphic functions P(ρ, P) depending on two parameters ρ and P introduced in [2]. These include as special cases the projective Schur, Nevanlinna and Carathéodory classes. A two sided Carathéodory - Fejér interpolation problem is defined and solved in P(ρ, P), using the fundamental matrix inequality method. A corresponding Schur algorithm is studied. Finally we also consider the case of functions (as opposed to pairs).

Original language	English
Pages (from-to)	17-69
Number of pages	53
Journal	Mathematische Nachrichten
Volume	199
DOIs	https://doi.org/10.1002/mana.19991990103
State	Published - 1 Jan 1999

ASJC Scopus subject areas

General Mathematics

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abstract = "We continue our study of families of pairs of matrix - valued meromorphic functions P(ρ, P) depending on two parameters ρ and P introduced in [2]. These include as special cases the projective Schur, Nevanlinna and Carath{\'e}odory classes. A two sided Carath{\'e}odory - Fej{\'e}r interpolation problem is defined and solved in P(ρ, P), using the fundamental matrix inequality method. A corresponding Schur algorithm is studied. Finally we also consider the case of functions (as opposed to pairs).",

author = "D. Alpay and V. Bolotnikov",

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AB - We continue our study of families of pairs of matrix - valued meromorphic functions P(ρ, P) depending on two parameters ρ and P introduced in [2]. These include as special cases the projective Schur, Nevanlinna and Carathéodory classes. A two sided Carathéodory - Fejér interpolation problem is defined and solved in P(ρ, P), using the fundamental matrix inequality method. A corresponding Schur algorithm is studied. Finally we also consider the case of functions (as opposed to pairs).

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ER -

Carathéodory - Fejér problem for pairs of meromorphic functions

Abstract

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