Strictly Positive Definite Functions on a Real Inner Product Space

Author： Pinkus Allan  

Publisher： Springer Publishing Company

ISSN： 1019-7168

Source： Advances in Computational Mathematics, Vol.20, Iss.4, 2004-05, pp. : 263-271

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Abstract

If f(t)=∑k=0∞aktk converges for all t∈R with all coefficients ak&0, then the function f(&〈x,y&〉) is positive definite on H×H for any inner product space H. Set k={k: ak>0}. We show that f(&〈x,y&〉) is strictly positive definite if and only if k contains the index 0 plus an infinite number of even integers and an infinite number of odd integers.

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