Gaussian RBF kernels via Fock spaces: quaternionic and several complex variables settings. (English) Zbl 07886850
Summary: 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.
MSC:
| 81-XX | Quantum theory |
| 30G35 | Functions of hypercomplex variables and generalized variables |
| 30H20 | Bergman spaces and Fock spaces |
| 44A15 | Special integral transforms (Legendre, Hilbert, etc.) |
| 46E20 | Hilbert spaces of continuous, differentiable or analytic functions |
Keywords:
reproducing Kernel Hilbert spaces; Gaussian RBF Kernel; RBF spaces quaternions; Fock space; several complex variables; Segal-Bargmann transformReferences:
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