# On a Fourier Expansion In Continuous Crossed Products

### Hiroshi Takai

Osaka University, Japan

## Abstract

Let (*M*, ℝ, *α*) be a separable continuous *W**-dynamical system such that *M* is ℝ-finite. Then any element in the crossed product ℝ ⊗α_M_ of *M* by α can be expressed as a vector valued tempered distribution *DqTη* which is a weak* limit of *Tε,ξ ∈ K(ℝ; ℬ) in the dual space SU(ℝ η)* of a generalized Schwartz space SU(ℝ η), where K(ℝ; ℬ) is the Tomita algebra corresponding to ℝ ⊗α_M*._

## Cite this article

Hiroshi Takai, On a Fourier Expansion In Continuous Crossed Products. Publ. Res. Inst. Math. Sci. 11 (1975), no. 3, pp. 849–880

DOI 10.2977/PRIMS/1195191150