We prove that any continuous function with domain {z ∈ C: |z| ≤ 1} that generates a bizonal positive definite kernel on the unit sphere in 'C POT.Q' , q ⩾ 3, is continuously differentiable in {z ∈ C: |z| < 1} up to order ...

We analyze reproducing kernel Hilbert spaces of positive definite kernels on a topological space X being either first countable or locally compact. The results include versions of Mercer's theorem and theorems on the ...

We study the action of a weighted Fourier–Laplace transform on the functions in the reproducing kernel Hilbert space (RKHS) associated with a positive definite kernel on the sphere. After defining a notion of smoothness ...

Multi-Output Gaussian Processes (MOGPs) are the multivariate extension of Gaussian processes (GPs \cite{Rasmussen:2006}), a Bayesian nonparametric method for univariate regression. MOGPs address the multi-channel regression ...

Associated with a given suitable function, or a measure, on R, we introduce a correlation function so that the Wronskian of the Fourier transform of the function is the Fourier transform of the corresponding correlation ...

Nowadays, the analysis of a large amount of data has emerged as an issue of great interest taking increasing place in the scientific community, especially in automation, signal processing, pattern recognition, and machine ...

Kernels methods provide a powerful and unifying framework to solve nonlinear problems while retaining in many cases, the simplicity of linear solutions. However, in machine learning and kernels methods, data is assumed to ...