Note on a result of Kerman and Weit

Mathematics – Functional Analysis

Scientific paper

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5 pages

Scientific paper

A result in \cite{Ker-Weit} states that a real valued continuous function $f$
on the circle and its nonnegative integral powers can generate a dense
translation invariant subspace in the space of all continuous functions on the
circle if $f$ has a unique maximum or a unique minimum. In this note we
endeavour to show that this is quite a general phenomenon in harmonic analysis.

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