Strongly mixing operators on Hilbert spaces and speed of mixing

2015/03/04 by Vincent Devinck, Devinck, Vincent · 1 citation
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1503.01341

38 pages

arxiv created 2015/03/04 · arxiv updated 2015/03/05

Abstract

We investigate the subject of speed of mixing for operators on infinite dimensional Hilbert spaces which are strongly mixing with respect to a nondegenerate Gaussian measure. We prove that there is no way to find a uniform speed of mixing for all square-integrable functions. We give classes of regular functions for which the sequence of correlations decreases to zero with speed n^-α when the eigenvectors associated to unimodular eigenvalues of the operator are parametrized by an α-Hölderian \mathbbT-eigenvector field.

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