S Wickramasekara and A Bohm 2002 J. Phys. A: Math. Gen. 35 807 doi:10.1088/0305-4470/35/3/322
S Wickramasekara and A Bohm
Show affiliationsWe 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.
81R15 Operator algebra methods (See also 46Lxx, 81T05)
47A70 (Generalized) eigenfunction expansions; rigged Hilbert spaces
22E60 Lie algebras of Lie groups (For the algebraic theory of Lie algebras, see 17Bxx)
Issue 3 (25 January 2002)
Received 29 March 2001, in final form 10 September 2001
Published 11 January 2002
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