# 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 $D_{q}T_{η}$ which is a weak$_{∗}$ limit of $T_{ξ}$, $ξ∈K(R;B)$ in the dual space $S_{U}(R;η)_{∗}$ of a generalized Schwartz space $S_{U}(R;η)$, 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