Positive definite norm dependent functions on l[infinity]

Jolanta K. Misiewicz

Statistics & Probability Letters, 1989, vol. 8, issue 3, 255-260

Abstract: It is well known that a function exp{z.sfnc;(max(z.sfnc;xz.sfnc;, z.sfnc;yz.sfnc;))[alpha]} is positive definite on 2 for every [alpha] [set membership, variant] (0, 1]. In paper we show that if n [greater-or-equal, slanted] 3 there is no positive definite norm dependent function on n with the supremum norm, except the constant. This statement gives a negative answer to a problem posed by Schoenberg (1938).

Keywords: positive; definite; functions; probability; distribution; Radon; transform; [alpha]-symmetric; distribution; norm; dependent; distribution (search for similar items in EconPapers)
Date: 1989
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