For a locally compact group, property RD gives a control on the convolution
norm of any compactly supported measure in terms of the $L^2$-norm of its
density and the diameter of its support. We give a complete classification of
those Lie groups with property RD.Comment: 29 page

Chatterji, I.

Pittet, Ch.

Saloff-Coste, L.

English

arXiv

For a locally compact group, the property of rapid decay (property RD) gives a control on the convolutor norm of any compactly supported function in terms of its L2-norm and the diameter of its support. We characterize the Lie groups that have pro-perty RD. The property of rapid decay (property RD) emerged from the work of U. Haagerup in [15] and was first studied systematically by P. Jolissaint in [21], mostly in the context of finitely generated groups. Property RD gives a control on the convolutor norm of any compactly supported function in terms of its L2-norm and the diameter of it

Connected Lie groups and property RD

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