Journal article
Norm-Constrained Determinantal Representations of Multivariable Polynomials
Complex analysis and operator theory, v 7(3), pp 635-654
01 Jun 2013
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
For every multivariable polynomial , with , we construct a determinantal representation, , where is a diagonal matrix with coordinate variables on the diagonal and is a complex square matrix. Such a representation is equivalent to the existence of whose principal minors satisfy certain linear relations. When norm constraints on are imposed, we give connections to the multivariable von Neumann inequality, Agler denominators, and stability. We show that if a multivariable polynomial , satisfies the von Neumann inequality, then admits a determinantal representation with a contraction. On the other hand, every determinantal representation with a contractive gives rise to a rational inner function in the Schur-Agler class.
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Details
- Title
- Norm-Constrained Determinantal Representations of Multivariable Polynomials
- Creators
- Anatolii Grinshpan - Drexel UniversityDmitry S. Kaliuzhnyi-Verbovetskyi - Drexel UniversityHugo J. Woerdeman - Drexel University
- Publication Details
- Complex analysis and operator theory, v 7(3), pp 635-654
- Publisher
- Springer Nature
- Number of pages
- 20
- Grant note
- DMS-0901628 / NSF; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000319472000007
- Scopus ID
- 2-s2.0-84878465613
- Other Identifier
- 991019168332404721
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- Web of Science research areas
- Mathematics
- Mathematics, Applied