Abstract
We consider in this note Furstenberg transformations on Cartesian products of infinite-dimensional tori. Under some appropriate assumptions, we show that these transformations are uniquely ergodic with respect to the Haar measure and have countable Lebesgue spectrum in a suitable subspace. These results generalise to the infinite-dimensional setting previous results of H. Furstenberg, A. Iwanik, M. Lemanzyk, D. Rudolph and the second author in the one-dimensional setting. Our proofs rely on the use of commutator methods for unitary operators and Bruhat functions on the infinite-dimensional torus.
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Supported by the Chilean Fondecyt Grant 1130168 and by the Iniciativa Cientifica Milenio ICM RC120002 “Mathematical Physics” from the Chilean Ministry of Economy.
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Cecchi, P.A., Tiedra de Aldecoa, R. Furstenberg Transformations on Cartesian Products of Infinite-Dimensional Tori. Potential Anal 44, 43–51 (2016). https://doi.org/10.1007/s11118-015-9497-y
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DOI: https://doi.org/10.1007/s11118-015-9497-y