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Volume 38, Issue 4, 2002, pp. 725–733
DOI: 10.2977/prims/1145476195

Published online: 2002-12-31

Quasianalyticity of Positive Definite Continuous Functions

Soon-Yeong Chung[1]

(1) Sogang University, Seoul, South Korea

It is shown that for a positive definite continuous function f(x) on ℝn the followings are equivalent:

  1. f(x) is quasianalytic in some neighborhood of the origin.
  2. f(x) can be expressed as an integral f(x) = ∫n eizξ (ξ) for some positive Radon measure μ on ℝn such that ∫ exp M (L|ξ|) (ξ) is finite for some L > 0 where the function M(t) is a weight function corresponding to the quasaianalyticity.
  3. f(x) is quasianalytic in ℝn
Moreover, an analogue for the analyticity is also given as a corollary.

Keywords: Positive definite, quasianalyticity

Chung Soon-Yeong: Quasianalyticity of Positive Definite Continuous Functions. Publ. Res. Inst. Math. Sci. 38 (2002), 725-733. doi: 10.2977/prims/1145476195