# Disjointness properties for Cartesian products of weakly mixing systems

Joanna Kułaga-Przymus; François Parreau

Colloquium Mathematicae (2012)

- Volume: 128, Issue: 2, page 153-177
- ISSN: 0010-1354

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topJoanna Kułaga-Przymus, and François Parreau. "Disjointness properties for Cartesian products of weakly mixing systems." Colloquium Mathematicae 128.2 (2012): 153-177. <http://eudml.org/doc/284268>.

@article{JoannaKułaga2012,

abstract = {For n ≥ 1 we consider the class JP(n) of dynamical systems each of whose ergodic joinings with a Cartesian product of k weakly mixing automorphisms (k ≥ n) can be represented as the independent extension of a joining of the system with only n coordinate factors. For n ≥ 2 we show that, whenever the maximal spectral type of a weakly mixing automorphism T is singular with respect to the convolution of any n continuous measures, i.e. T has the so-called convolution singularity property of order n, then T belongs to JP(n-1). To provide examples of such automorphisms, we exploit spectral simplicity on symmetric Fock spaces. This also allows us to show that for any n ≥ 2 the class JP(n) is essentially larger than JP(n-1). Moreover, we show that all members of JP(n) are disjoint from ergodic automorphisms generated by infinitely divisible stationary processes.},

author = {Joanna Kułaga-Przymus, François Parreau},

journal = {Colloquium Mathematicae},

keywords = {disjointness; joinings; spectral singularity and convolutions; spectral simplicity; infinite divisibility},

language = {eng},

number = {2},

pages = {153-177},

title = {Disjointness properties for Cartesian products of weakly mixing systems},

url = {http://eudml.org/doc/284268},

volume = {128},

year = {2012},

}

TY - JOUR

AU - Joanna Kułaga-Przymus

AU - François Parreau

TI - Disjointness properties for Cartesian products of weakly mixing systems

JO - Colloquium Mathematicae

PY - 2012

VL - 128

IS - 2

SP - 153

EP - 177

AB - For n ≥ 1 we consider the class JP(n) of dynamical systems each of whose ergodic joinings with a Cartesian product of k weakly mixing automorphisms (k ≥ n) can be represented as the independent extension of a joining of the system with only n coordinate factors. For n ≥ 2 we show that, whenever the maximal spectral type of a weakly mixing automorphism T is singular with respect to the convolution of any n continuous measures, i.e. T has the so-called convolution singularity property of order n, then T belongs to JP(n-1). To provide examples of such automorphisms, we exploit spectral simplicity on symmetric Fock spaces. This also allows us to show that for any n ≥ 2 the class JP(n) is essentially larger than JP(n-1). Moreover, we show that all members of JP(n) are disjoint from ergodic automorphisms generated by infinitely divisible stationary processes.

LA - eng

KW - disjointness; joinings; spectral singularity and convolutions; spectral simplicity; infinite divisibility

UR - http://eudml.org/doc/284268

ER -

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