Interpolation sets for convolution measure algebras

Graham, Colin C.

doi:10.1090/S0002-9939-1973-0318778-8

Interpolation sets for convolution measure algebras
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by Colin C. Graham PDF

Proc. Amer. Math. Soc. 38 (1973), 512-522 Request permission

Abstract:

These are proved: (1) The union of two interpolation sets for a regular commutative convolution measure algebra is not necessarily an interpolation set. (2) There exists a regular commutative convolution measure algebra for which interpolation sets are not necessarily of spectral synthesis, while every singleton is a Ditkin set. (3) For every nondiscrete LCA group $G$, there exist compact interpolation sets for $M(G)$ whose union is not an interpolation set. A tensor algebra method is used.

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Commutative normed rings

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A pseudofunction on a Helson set