Abstract
Let G be a compact connected semisimple Lie group with Lie algebra g. We show that the conjugacy class of a regular element of G is not a set of synthesis for the Fourier algebra of G. Similarly, the Ad(G)-orbit of a regular element of g is not a set of synthesis for the algebra of Fourier transforms on g. In proving this latter result we demonstrate a regularity property of Ad-invariant Fourier transforms, analogous to the differentiability of radial Fourier transforms.
| Original language | English |
|---|---|
| Pages (from-to) | 43-57 |
| Number of pages | 15 |
| Journal | Journal of Functional Analysis |
| Volume | 48 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1982 |
| Externally published | Yes |
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Cite this
Meaney, C. (1982). On the failure of spectral synthesis for compact semisimple Lie groups. Journal of Functional Analysis, 48(1), 43-57. https://doi.org/10.1016/0022-1236(82)90060-X