We use methods from the Fock space and Segal-Bargmann theories to prove
several results on the Gaussian RBF kernel in complex analysis. The latter is
one of the most used kernels in modern machine learning kernel methods, and in
support vector machines (SVMs) classification algorithms. Complex analysis
techniques allow us to consider several notions linked to the RBF kernels like
the feature space and the feature map, using the so-called Segal-Bargmann
transform. We show also how the RBF kernels can be related to some of the most
used operators in quantum mechanics and time frequency analysis, specifically,
we prove the connections of such kernels with creation, annihilation, Fourier,
translation, modulation and Weyl operators. For the Weyl operators, we also
study a semigroup property in this case.
