An extension of Herglotz's theorem to the quaternions (Q401402)
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scientific article; zbMATH DE number ?
- Wiener algebra for the quaternions
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| English | An extension of Herglotz's theorem to the quaternions |
scientific article; zbMATH DE number ? |
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An extension of Herglotz's theorem to the quaternions (English)
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Wiener algebra for the quaternions (English)
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26 August 2014
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7 December 2016
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The authors are interested in a quaternionic analog of the classical theorem of Herglotz of one-dimensional complex analysis. Specifically, they consider the case when the function is allowed to have a number of negative squares. The approach is based on the theory of slice hyperholomorphic functions, and the representation of such functions which have a positive real part in the unit ball of the quaternions.
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Bochner theorem
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Herglotz integral representation theorem
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negative squares
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Pontryagin spaces
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reproducing kernels
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slice hyperholomorphic functions
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quaternions
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Wiener algebras
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Toeplitz operators
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Wiener-Hopf operators
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0.91507185
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0.9012855
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0.89815605
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