caa a22 4500 386307636 CHVBK 20180307111534.0 cr unu---uuuuu 161130e198808 xx s 000 0 eng 10.1017/S1446788700032225 doi S1446788700032225 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700032225 Ward J. A. School of Mathematical and Physical Sciences Murdoch University Perth, Western Australia 6153, Australia Analytic functions which operate on homogeneous algebras [Elektronische Daten] [J. A. Ward] It is well known that a complex-valued function ø, analytic on some open set Ω, extends to any commutative Banach algebra B so that the action of ø on B commutes with the action of the Gelfand transformation. In this paper, it is shown that if B is a homogeneous convolution Banach algebra over any compact group and if 0 Ω is a fixed point of ø, then a similar result holds, with the Gelfand transformation replaced by the Fourier-Stieltjes transformation. Care is required, in that discussion of this relation usually requires simultaneous consideration of the extension of ø to B and to certain operator algebras. Copyright © Australian Mathematical Society 1988 primary 43 A 10 nationallicence secondary 43 A 15 nationallicence 46 H 30 nationallicence Journal of the Australian Mathematical Society Cambridge University Press 45/1(1988-08), 1-10 1446-7887 45:1<1 1988 45 JAZ https://doi.org/10.1017/S1446788700032225 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700032225 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Ward J. A. School of Mathematical and Physical Sciences Murdoch University Perth, Western Australia 6153, Australia NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 45/1(1988-08), 1-10 1446-7887 45:1<1 1988 45 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge