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 on the followings are equivalent:

  1. is quasianalytic in some neighborhood of the origin.
  2. can be expressed as an integral for some positive Radon measure on such that is finite for some where the function is a weight function corresponding to the quasaianalyticity.
  3. is quasianalytic in .

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