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On the collection of spectral multiplicities \(\{2, 4,\dots,2^n\}\) for totally ergodic \(\mathbb Z^2\)-actions. (English. Russian original) Zbl 1370.37062
Math. Notes 96, No. 3, 360-368 (2014); translation from Mat. Zametki 96, No. 3, 383-392 (2014).
Summary: The paper is devoted to the realization of collections of spectral multiplicities for ergodic \(\mathbb Z^2\)-actions. Sufficient conditions ensuring the realizability of multiplicities of the form \(\{2,4,\dots,2^n\}\) are given.

MSC:
37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\)
37A30 Ergodic theorems, spectral theory, Markov operators
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