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Positive definite norm dependent functions on l[infinity]

Author

Listed:
  • Misiewicz, Jolanta K.

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).

Suggested Citation

  • Misiewicz, Jolanta K., 1989. "Positive definite norm dependent functions on l[infinity]," Statistics & Probability Letters, Elsevier, vol. 8(3), pages 255-260, August.
    • Handle: RePEc:eee:stapro:v:8:y:1989:i:3:p:255-260
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