Vol. 73, No. 2, 1977

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The Fourier transform for nilpotent locally compact groups. I

Roger Evans Howe

Vol. 73 (1977), No. 2, 307–327

In his work on nilpotent lie groups, A. A. Kirillov introduced the idea of classifying the representations of such groups by matching them with orbits in the dual of the lie algebra under the coadjoint action. His methods have proved extremely fruitful, and subsequent authors have refined and extended them to the point where they provide highly satisfactory explanations of many aspects of the harmonic analysis of various lie groups. Meanwhile, it appears that nonlie groups are also amenable to such an approach. In this paper, we seek to indicate that, indeed, a very large class of separable, locally compact, nilpotent groups have a Kirillov-type theory.

Mathematical Subject Classification 2000
Primary: 22D12
Received: 21 May 1977
Published: 1 December 1977
Roger Evans Howe