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The spectral type of the staircase transformation. (English) Zbl 0853.28008
We show that a certain Riesz-product type measure is singular with respect to Lebesgue measure on the circle. This proves the singularity of the spectral measures of a certain ergodic map known as the staircase transformation.

MSC:
28D05 Measure-preserving transformations
42A55 Lacunary series of trigonometric and other functions; Riesz products
47A35 Ergodic theory of linear operators
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[1] T. M. ADAMS, Smorodinsky’sconjecture, preprint(1993).
[2] T. M. ADAMS AND N. A. FRIEDMAN, Staircase mixing, Ergodic Th. & Dynam.Sys (to appear).
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