  Positive definite functions are fundamental to many areas of applied
mathematics, probability theory, spatial statistics and machine learning,
amogst others. Motivated by a problem coming from the maximum likelihood
estimation under fixed domain asymptotics, we consider a new operator acting on
rescaled weighted differences between two members of the class $\Phi_d$ of
positive definite radial functions,. In particular, we study the positive
definiteness of the operator for the Mat\'ern, Generalized Cauchy and
Generalized Wendland families. It turns out that proposed operator allows to
govern differentiability at the origin, and to attain negative correlations.
