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Focusing on quaternionic linear operators, this work explores their unique properties compared to complex operators, particularly in the noncommutative realm. It introduces concepts like the S-spectrum and S-resolvent operators while examining de Branges spaces, which serve as quaternionic analogs of analytic function spaces. The study emphasizes specific reproducing kernels in the unit ball or half-space of quaternions, delving into Hilbert, Pontryagin, and Krein spaces and their connections to operator models.
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Quaternionic de Branges Spaces and Characteristic Operator Function, Daniel Alpay, Fabrizio Colombo, Irene Sabadini
- Language
- Released
- 2020
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- (Paperback)
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- Title
- Quaternionic de Branges Spaces and Characteristic Operator Function
- Language
- English
- Authors
- Daniel Alpay, Fabrizio Colombo, Irene Sabadini
- Publisher
- Springer International Publishing
- Released
- 2020
- Format
- Paperback
- Pages
- 128
- ISBN13
- 9783030383114
- Category
- Mathematics
- Description
- Focusing on quaternionic linear operators, this work explores their unique properties compared to complex operators, particularly in the noncommutative realm. It introduces concepts like the S-spectrum and S-resolvent operators while examining de Branges spaces, which serve as quaternionic analogs of analytic function spaces. The study emphasizes specific reproducing kernels in the unit ball or half-space of quaternions, delving into Hilbert, Pontryagin, and Krein spaces and their connections to operator models.