On the roots of determinants of a class of holomorphic matrix-valued functions

We consider matrix-valued functions that are holomorphic in the unit disk that are Cauchy transforms of finite matrix-valued measures. For non-zero roots zj of the determinants of such functions, we provide estimates for ∑(|zj|−1−1) and [∑(|zj|−1−1)2]1/2.

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Published inJournal of mathematical analysis and applications Vol. 408; no. 1; pp. 291 - 297
Main Author Bekker, Miron B.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.12.2013
Subjects
Blaschke condition
Cauchy transform
Determinant
Hilbert–Schmidt norm
Holomorphic matrix-valued function
Roots
Trace norm
Cauchy transform
Hilbert–Schmidt norm
Determinant
Roots
Trace norm
Blaschke condition
Holomorphic matrix-valued function
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Abstract We consider matrix-valued functions that are holomorphic in the unit disk that are Cauchy transforms of finite matrix-valued measures. For non-zero roots zj of the determinants of such functions, we provide estimates for ∑(|zj|−1−1) and [∑(|zj|−1−1)2]1/2.
AbstractList We consider matrix-valued functions that are holomorphic in the unit disk that are Cauchy transforms of finite matrix-valued measures. For non-zero roots zj of the determinants of such functions, we provide estimates for ∑(|zj|−1−1) and [∑(|zj|−1−1)2]1/2.
Author Bekker, Miron B.
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10.1090/surv/125
10.1016/j.jmaa.2006.05.002
10.1007/s11005-011-0494-9
10.1112/blms/bds067
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Keywords Cauchy transform
Hilbert–Schmidt norm
Determinant
Roots
Trace norm
Blaschke condition
Holomorphic matrix-valued function
Language English
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Snippet We consider matrix-valued functions that are holomorphic in the unit disk that are Cauchy transforms of finite matrix-valued measures. For non-zero roots zj of...
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StartPage 291
SubjectTerms Blaschke condition
Cauchy transform
Determinant
Hilbert–Schmidt norm
Holomorphic matrix-valued function
Roots
Trace norm
Title On the roots of determinants of a class of holomorphic matrix-valued functions
URI https://dx.doi.org/10.1016/j.jmaa.2013.02.055
Volume 408
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