1. CMB 2006 (vol 49 pp. 203)
|The Ergodic Hilbert Transform for Admissible Processes |
It is shown that the ergodic Hilbert transform exists for a class of bounded symmetric admissible processes relative to invertible measure preserving transformations. This generalizes the well-known result on the existence of the ergodic Hilbert transform.
Keywords:Hilbert transform, admissible processes
2. CMB 2002 (vol 45 pp. 123)
|Uniform Distribution in Model Sets |
We give a new measure-theoretical proof of the uniform distribution property of points in model sets (cut and project sets). Each model set comes as a member of a family of related model sets, obtained by joint translation in its ambient (the `physical') space and its internal space. We prove, assuming only that the window defining the model set is measurable with compact closure, that almost surely the distribution of points in any model set from such a family is uniform in the sense of Weyl, and almost surely the model set is pure point diffractive.
Categories:52C23, 11K70, 28D05, 37A30
3. CMB 2000 (vol 43 pp. 157)
|A Larger Class of Ornstein Transformations with Mixing Property |
We prove that Ornstein transformations are almost surely totally ergodic provided only that the cutting parameter is not bounded. We thus obtain a larger class of Ornstein transformations with the mixing property.