Geodesic
On the Collection of Spectral Multiplicities $\{2,4,\dots,2^n\}$ for Totally Ergodic $\mathbb{Z}^2$-Actions
Matematičeskie zametki, Tome 96 (2014) no. 3, pp. 383-392

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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.
Keywords: collection of spectral multiplicities $\{2,4,\dots,2^n\}$, ergodic $\mathbb{Z}^2$-action, spectral multiplicity of an ergodic action, linear envelope, cyclic vector. 
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     author = {R. A. Konev and V. V. Ryzhikov},
     title = {On the {Collection} of {Spectral} {Multiplicities} $\{2,4,\dots,2^n\}$ for {Totally} {Ergodic} $\mathbb{Z}^2${-Actions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {383--392},
     publisher = {mathdoc},
     volume = {96},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_3_a7/}
}
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R. A. Konev; V. V. Ryzhikov. On the Collection of Spectral Multiplicities $\{2,4,\dots,2^n\}$ for Totally Ergodic $\mathbb{Z}^2$-Actions. Matematičeskie zametki, Tome 96 (2014) no. 3, pp. 383-392. http://geodesic.mathdoc.fr/item/MZM_2014_96_3_a7/