Recurrence relations for radial positive definite functions (Q1849144)

In the theory of radial basis functions as well as in the theory of spherically symmetric characteristic functions, recurrence relations are used to construct \(d\)-dimensional functions starting with lower-dimensional ones. The author shows that the operators used so far are special cases of one-step recurrence relations for \(\ell_2\)-radial positive definite functions. He further gives the analogue for \(\ell_1\)-radial functions and thereby defines a turning bands operator for 1-symmetric characteristic functions.