Completeness in irreducible representations of compact groups

For we have

(1)

See [eq. ( IZ80, p.3.1 )] for this form and [Vil68, p.46 eqs. (4), (5 )] for its consequence — Fourier transform on compact group

(2)

where

(3)

References

[IZ80]

C. Itzykson and J.-B. Zuber, “The planar approximation. ii,” J. Math. Phys., vol. 21, no. 3, pp. 411–421, 1980, doi: 10.1063/1.524438.

[Vil68]

N. J. Vilenkin, Special functions and the theory of group representations, Revised. American Mathematical Society, 1968.