# Quasianalyticity of Positive Definite Continuous Functions

### Soon-Yeong Chung

Sogang University, Seoul, South Korea

## Abstract

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*) = ∫ℝ_n_*eizξ**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_

Moreover, an analogue for the analyticity is also given as a corollary.

## Cite this article

Soon-Yeong Chung, Quasianalyticity of Positive Definite Continuous Functions. Publ. Res. Inst. Math. Sci. 38 (2002), no. 4, pp. 725–733

DOI 10.2977/PRIMS/1145476195