Gaussian RBF kernels via Fock spaces: quaternionic and several complex variables settings

In this paper, we study two extensions of the complex-valued Gaussian radial basis function (RBF) kernel and discuss their connections with Fock spaces in two different settings. First, we introduce the quaternionic Gaussian RBF kernel constructed using the theory of slice hyperholomorphic functions...

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Veröffentlicht in:	Quantum Studies : Mathematics and Foundations 2024-04, Vol.11 (1), p.69-85
Hauptverfasser:	De Martino, Antonino, Diki, Kamal
Format:	Artikel
Sprache:	eng
Schlagworte:	Complex variables History and Philosophical Foundations of Physics Mathematical and Computational Physics Mathematical Physics Mathematics Mathematics and Statistics Quantum Physics Radial basis function Regular Paper Theoretical
Online-Zugang:	Volltext
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Zusammenfassung:	In this paper, we study two extensions of the complex-valued Gaussian radial basis function (RBF) kernel and discuss their connections with Fock spaces in two different settings. First, we introduce the quaternionic Gaussian RBF kernel constructed using the theory of slice hyperholomorphic functions. Then, we consider the case of Gaussian RBF kernels in several complex variables.
ISSN:	2196-5609 2196-5617
DOI:	10.1007/s40509-024-00318-7