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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.


This article was originally published in Quantum Studies: Mathematics and Foundations, volume 11, in 2024.

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Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.



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