Schur functions and their realizations in the slice hyperholomorphic setting (Q421113)
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scientific article; zbMATH DE number 6038030
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Schur functions and their realizations in the slice hyperholomorphic setting |
scientific article; zbMATH DE number 6038030 |
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Schur functions and their realizations in the slice hyperholomorphic setting (English)
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23 May 2012
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The authors develop Schur analysis, including the Schur algorithm and a theory of linear systems, in the context of the skew-field of quaternions. The basic tool is the theory of slice hyperholomorphic functions, which allow to write realizations in terms of a suitable resolvent. Results holding in the complex case are extended to the quaternionic one. Reproducing kernels, positive definite functions, and Schur multipliers are also discussed in this setting.
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Schur functions
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realizations
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reproducing kernels
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slice hyperholomorphic functions
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S-resolvent operators
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