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Analytic functions which operate on homogeneous algebras

Ward, J.A. (1988) Analytic functions which operate on homogeneous algebras. Journal of the Australian Mathematical Society, 45 (01). pp. 1-10.

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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 ϵ 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.

Publication Type: Journal Article
Murdoch Affiliation: School of Mathematical and Physical Sciences
Publisher: Cambridge University Press
Copyright: © 1988, Australian Mathematical Society
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