nLab Peter-Weyl theorem

Idea

Representative functions on a compact topological group form a dense subspace of the space of all continuous functions.

References

Textbook account:

• Tammo tom Dieck, Theodor Bröcker, Sections III.3, III.4 in: Representations of compact Lie groups, Springer 1985 (doi:10.1007/978-3-662-12918-0)

Lecture notes:

• Linus Kramer, Section 3 of: Locally Compact Groups, 2017 (pdf, pdf)

See also:

• Wikipedia, Peter-Weyl theorem