Abstract
We imbed the space of pseudo-measuresA′(E) supported by a closed totally disconnected setE\( \subseteq \)R/2πZ into a space of distributions on an “imbedding” group. The basic technique is to find a sequence of measuresμm onE (non discrete measures generally) associated with eachT∈A′(E), so that, with an additional arithmetic condition, {μm} converges in a weaker than weak * topology to a measure μ, and μ=T. Using this framework we prove that a Helson set is a set of spectral synthesis if and only if certain of our distributions have a support preserving extension. We also introduce a uniqueness criterion, and show that the extension condition and uniqueness condition imply thatA′(E) is the space of measures supported byE.
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