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 |
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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 |