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Strongly mixing operators on Hilbert spaces and speed of mixing
Author(s) -
Devinck Vincent
Publication year - 2013
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pds081
Subject(s) - mathematics , mixing (physics) , unimodular matrix , eigenvalues and eigenvectors , hilbert space , operator (biology) , mathematical analysis , pure mathematics , measure (data warehouse) , zero (linguistics) , quantum mechanics , physics , biochemistry , chemistry , linguistics , philosophy , repressor , database , computer science , transcription factor , gene
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 ‐eigenvector field.
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