The Classes N(X) and RPD(X) : Integral Representations
This chapter continues the study of radial positive definite functions and functions of negative type begun in the preceding chapter. Following methods introduced by Schoenberg [79,80,81] and recently refined by Bretagnolle, Dacunha Castelle, and Krivine , and Kuelbs , we are going to present characterizations of the classes RPD(X) and N(X) when X is one of the spaces ℝ n or L p (n = 1,2, … ; 0 < p ≤ ∞ ).
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