Some applications of Boolean valued set theory to abstract harmonic analysis on locally compact groups (Q1069087)

The object of this paper is to extend abstract harmonic analysis on locally compact abelian groups to more general locally compact groups by using Boolean valued technique. In {\S} 2, the author gives a brief review of Boolean valued set theory. {\S} 3 contains the result: a unitary representation \(\gamma\) (\(\gamma\) : \(G\to\) the group of unitary operators of a Hilbert space H) of a locally compact group G is irreducible in a Boolean valued universe \(V^{(B)}\), where B is a Boolean algebra of projections of H with some additional property. In {\S} 4, by Boolean valued argument, the author proves that every positive definite function on G is regarded as the Fourier transform which corresponds to Bochner's well-known theorem.