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If K is not compact, then the algebra of bi-K-invariant continuous functions on G is not very meaningful as there aren't many bi-K-invariant compactly supported functions on G... It is also not so clear what is the analogue of this algebra in this case, see e.g. https://arxiv.org/pdf/1807.02843 (also: https://academic.oup.com/imrn/article-abstract/2021/12/9203/5513962?redirectedFrom=fulltext&login=false).

I suggest to restrict the generality to the case where K is compact. 5.22.130.218 (talk) 15:20, 2 March 2025 (UTC)[reply]