Klemes, Ivo The spectral type of the staircase transformation. (English) Zbl 0853.28008 Tôhoku Math. J., II. Ser. 48, No. 2, 247-258 (1996). 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. Reviewer: I.Klemes (Montreal) Cited in 7 Documents MSC: 28D05 Measure-preserving transformations 42A55 Lacunary series of trigonometric and other functions; Riesz products 47A35 Ergodic theory of linear operators Keywords:Riesz products; singular measures; Riesz-product type measure; ergodic map; staircase transformation PDF BibTeX XML Cite \textit{I. Klemes}, Tohoku Math. J. (2) 48, No. 2, 247--258 (1996; Zbl 0853.28008) Full Text: DOI References: [1] T. M. ADAMS, Smorodinsky’sconjecture, preprint(1993). [2] T. M. ADAMS AND N. A. FRIEDMAN, Staircase mixing, Ergodic Th. & Dynam.Sys (to appear). [3] J. BOURGAIN, On the spectral type of Ornstein’sclass one transformations, Israel J. Math. 8 (1993), 53-63. · Zbl 0787.28011 · doi:10.1007/BF02761690 [4] J. CHOKSI AND M. NADKARNI, The maximal spectral type of a rank on transformation, Canadian Math. Bull. 37 (1993), 29-36. · Zbl 0793.28013 · doi:10.4153/CMB-1994-005-4 [5] G. H. HARDY AND E. M. WRIGHT, ”An introduction to the theory of numbers”, Oxford, 1945, 2nd ed. · Zbl 0058.03301 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.