Research Article

Fourier transforms and descriptive set theory

R. Kaufmana1

a1 Department of Mathematics, University of Illinois, 273 Altgeld Hall, 1409, West Green Street, Urbana, Illinois, 61801, U.S.A.

We state some definitions belonging to the two halves of the title, going far enough to state our main results.

Fourier transforms. Let μ be a finite, complex-valued measure on R and its Fourier-Stieltjes transform. We define to be the set of μ with When μ and φ is of class (continuously differentiable of compact support), the identity shows that θ · μ .

(Received May 15 1984)

Key Words:

  • 54H05: GENERAL TOPOLOGY; Connections with other structures, applications; Descriptive set theory