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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Bibliographic Details
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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Summary: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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2013.02.055