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PROPERTIES OF CERTAIN SUBALGEBRAS OF DALES-DAVIE ALGEBRAS

2007
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Glasgow Mathematical Journal
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We study an interesting class of Banach function algebras of infinitely differentiable functions on perfect, compact plane sets. These algebras were introduced by H. G. Dales and A. M. Davie in 1973, called Dales-Davie algebras and denoted by D(X, M), where X is a perfect, compact plane set and M = {M n } ∞ n=0 is a sequence of positive numbers such that M 0 = 1 and (m We show that, under certain conditions on X, every f ∈ D(X, M) has an analytic extension to X d . Let D P [D R ] be the

doi:10.1017/s0017089507003576
fatcat:e2goz4w725az3g2tljxoxiwwry