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I have been looking for an analog of the Fourier transform for groupoids coming from tilings (which are generally principal and r-discrete), however all the generalizations I have found assume that the groupoid:

  1. is compact (

  2. is a group bundle ( pg 3632

  3. is decomposable ( section 7.

Are there any versions of the Fourier transform for a principal r-discrete groupoid?

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No ideas? Even just a comment that this has not been studied would be helpful. – mkreisel Jul 28 '13 at 18:41

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