# Publications of the Research Institute for Mathematical Sciences

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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 ℝ^{n} the followings are equivalent:

*f*(*x*) is quasianalytic in some neighborhood of the origin.*f*(*x*) can be expressed as an integral*f*(*x*) = ∫_{ℝn}*e*^{izξ}*dμ*(*ξ*) for some positive Radon measure*μ*on ℝ^{n}such that ∫ exp*M (L|ξ|)*is finite for some*dμ*(*ξ*)*L*> 0 where the function*M*(*t*) is a weight function corresponding to the quasaianalyticity.*f*(*x*) is quasianalytic in ℝ^{n}

*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