Conference proceeding
Rational Inner Functions on a Square-Matrix Polyball
HARMONIC ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, BANACH SPACES, AND OPERATOR THEORY, VOL 2: CELEBRATING CORA SADOSKY'S LIFE, v 5
01 Jan 2017
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
We establish the existence of a finite-dimensional unitary realization for every matrix-valued rational inner function from the Schur-Agler class on a unit square-matrix polyball. In the scalar-valued case, we characterize the denominators of these functions. We also show that a multiple of every polynomial with no zeros in the closed domain is such a denominator. One of our tools is the Koranyi-Vagi theorem generalizing Rudin's description of rational inner functions to the case of bounded symmetric domains; we provide a short elementary proof of this theorem suitable in our setting.
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Details
- Title
- Rational Inner Functions on a Square-Matrix Polyball
- Creators
- Anatolii Grinshpan - Drexel UniversityDmitry S. Kaliuzhnyi-Verbovetskyi - Drexel UniversityVictor Vinnikov - Ben-Gurion University of the NegevHugo J. Woerdeman - Drexel University
- Contributors
- M C Pereyra (Editor)S Marcantognini (Editor)A M Stokolos (Editor)W Urbina (Editor)
- Publication Details
- HARMONIC ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, BANACH SPACES, AND OPERATOR THEORY, VOL 2: CELEBRATING CORA SADOSKY'S LIFE, v 5
- Series
- Association for Women in Mathematics Series
- Publisher
- Springer Nature
- Number of pages
- 11
- Grant note
- 2010432 / BSF; US-Israel Binational Science Foundation DMS-0901628 / NSF; National Science Foundation (NSF)
- Resource Type
- Conference proceeding
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000578301400010
- Scopus ID
- 2-s2.0-85071506266
- Other Identifier
- 991019168698804721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics