Abstract
Rank one transformations are transformations which can be obtained by cutting and stacking, using a single column in each step. Such a transformation is defined by a sequence of cutting parameters (p k ) k≥1 and a sequence of parameters of spacers . Rank one transformations are ergodic and have simple spectrum. By a result of Klemes and Reinhold, a rank one transformation is of singular maximal spectral type if . El Abdalaoui showed that for arbitrary (p k ) k≥1 the transformation has singular maximal spectral type if for each k all the numbers are of different order of magnitude. In this article we prove a counterpart of El Abdalaoui's result: if for infinitely many indices k a certain (relatively small) proportion of the coefficients are all equal, then the transformation is of singular maximal spectral type.
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