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Zeitschrift für Analysis und ihre Anwendungen

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Volume 5, Issue 5, 1986, pp. 457–463
DOI: 10.4171/ZAA/214

Published online: 1986-10-31

Zum Begriff der Analytizität auf zusammenhängenden Iokalkompakten Gruppen

Hans F. Bauch[1]

(1) Ernst-Moritz-Arndt-Universität Greifswald, Germany

Several definitions of analyticity of functions on locally compact groups are introduced and tested in connection with the proprties of the Fourier coefficients on a compact solenoid. It is proved that absolute convergence of the Fourier series does not follow from analyticity and that a rapidly decreasing sequence of Fourier coefficients of a function, which is analytic on a dense subset, need not exponentially rapidly decrease. On the other hand, on compact groups functions with exponentially rapidly decreasing Fourier coefficients are analytic.

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Bauch Hans: Zum Begriff der Analytizität auf zusammenhängenden Iokalkompakten Gruppen. Z. Anal. Anwend. 5 (1986), 457-463. doi: 10.4171/ZAA/214