Vol. 108, No. 1, 1983

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A property of some Fourier-Stieltjes transforms

Hiroshi Yamaguchi

Vol. 108 (1983), No. 1, 243–256

Helson and Lowdenslager extended the classical F. and M. Riesz theorem as follows:

Let G be a compact abelian group with the ordered dual Ĝ. Let μ be a bounded regular measure on G which is of analytic type. Then μa and μs are of analytic type.

Doss extended this theorem for a LCA group with the algebraically ordered dual. On the other hand, deLeeuw and Glicksberg obtained an analogous result for a compact abelian group G such that there exists a nontrivial homomorphism from Ĝ into R. In this paper, we prove that the theorem of Helson and Lowdenslager is satisfied for a LCA group with partially ordered dual.

Mathematical Subject Classification 2000
Primary: 43A17
Secondary: 43A05
Received: 9 March 1981
Revised: 10 May 1982
Published: 1 September 1983
Hiroshi Yamaguchi