Abstract. We discuss some basic properties of Lie group representations in rigged Hilbert spaces. In particular, we show that a differentiable representation in a rigged Hilbert space may be obtained as the projective limit of a family of continuous representations in a nested scale of Hilbert spaces. We also construct a couple of examples illustrative of the key features of group representations in rigged Hilbert spaces. Finally, we establish a simple criterion for the integrability of an operator Lie algebra in a rigged Hilbert space.

PACS numbers: 02.20.−a, 02.30.Sa

Print publication: Issue 3 (25 January 2002)
Received 29 March 2001, in final form 10 September 2001
Published 11 January 2002