3 problems

Ma's conjecture. Theorem 4 should hold in the stated generality: the Euclidean isotropic covariance matrix function and the corresponding covariance matrix functions obtained using…

Let $C$ be the covariance function of a real homogeneous isotropic random field on $d$-dimensional Euclidean space. The covariance function is not assumed a priori to be continuous…

Schoenberg's conjecture. The only discontinuity that an isotropic covariance function on $\mathbb{R}^{d}$ can have occurs at the origin; equivalently, it admits the decomposition a…