Murdoch University Research Repository

Welcome to the Murdoch University Research Repository

The Murdoch University Research Repository is an open access digital collection of research
created by Murdoch University staff, researchers and postgraduate students.

Learn more

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.

[img]
Preview
PDF - Published Version
Download (407kB) | Preview
Link to Published Version: http://dx.doi.org/10.1017/S1446788700032225
*Subscription may be required

Abstract

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.

Item Type: Journal Article
Murdoch Affiliation: School of Mathematical and Physical Sciences
Publisher: Cambridge University Press
Copyright: © 1988, Australian Mathematical Society
URI: http://researchrepository.murdoch.edu.au/id/eprint/30307
Item Control Page Item Control Page

Downloads

Downloads per month over past year