The connection between analyticity of functions on a compact connected group and the properties of their Fourier coefficients is lnvestigated.The functions with exponentially rapidly decreasing Fourier coefficients are exactly the analytic vectors of the right regular representation with the representation space of the functions with absolutely convergent Fourier series.They also can be continued analytically in the complexification of the group.
Cite this article
Hans F. Bauch, Paley-Wiener-Sätze auf kompakten topologischen Gruppen. Z. Anal. Anwend. 10 (1991), no. 2, pp. 211–224DOI 10.4171/ZAA/444