The characterization of Fourier series of real analytic functions and hyperfunctions on compact Lie groups is discussed by means of complex analysis.
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Yutaka Saburi, A Complex Analytic Study on the Theory of Fourier Series on Compact Lie Groups. Publ. Res. Inst. Math. Sci. 33 (1997), no. 6, pp. 953–966DOI 10.2977/PRIMS/1195144883