Toeplitz \(Z_ 2\)-extensions. (English) Zbl 0647.28013

Lemańczyk, Mariusz

Ann. Inst. Henri Poincaré, Probab. Stat. 24, No. 1, 1-43 (1988).

The author considers a class of ergodic automorphisms which are \(Z_ 2\)- extensions of automorphisms with rational discrete spectrum. In the early part of the paper the class is described and conditions are given for various spectral properties, including boundedness of the spectral multiplicity.
The majority of the paper deals in detail with various subclasses, such as generalized Morse sequences. Of special interest are some examples with a Lebesgue spectral component of finite (even) multiplicity.

Reviewer: D.Newton

MSC:

28D05

Measure-preserving transformations

Keywords:

ergodic automorphisms; \(Z_ 2\)-extensions; spectral multiplicity; generalized Morse sequences; Lebesgue spectral component