Ergodic Abelian actions with homogeneous spectrum

2010/01/13 by Alexandre I. Danilenko, Danilenko, Alexandre I., Anton V. Solomko +1
Mathematics · #Advanced Topology and Set Theory #advanced mathematical theories #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1001.2259

Abstract

It is shown that for each N>0 and for a wide class of Abelian non-compact locally compact second countable groups G including all infinite countable discrete ones and \Bbb R^d₁×\Bbb Z^d₂ with d₁,d₂≥ 0, there exists a weakly mixing probability preserving G-action with a homogeneous spectrum of multiplicity N.

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