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Disjointness properties for Cartesian products of weakly mixing systems

100%

Kułaga-Przymus J., Parreau F.

Colloquium Mathematicum

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2012

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tom 128

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nr 2

153-177

EN

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.

2

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The generalized purity law for ergodic measures: a simple proof

80%

Host B., Parreau F.

Colloquium Mathematicum

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1990

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tom 60-61

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nr 1

205-212

3

Sur les supports des transformées de Fourier-Stieltjes

70%

Graham C. C., Host B., Parreau F.

Colloquium Mathematicum

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1981

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tom 44

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nr 1

145-146

4

Spectres joints et prolongement des caractères

41%

Host B., Parreau F.

Studia Mathematica

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1982

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tom 73

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nr 1

63-74

Ograniczanie wyników

3 Colloquium Mathematicum

1 Studia Mathematica

4 Parreau F.

3 Host B.

1 Graham C. C.

1 Kułaga-Przymus J.

1 2012

1 1990

1 1982

1 1981

Disjointness properties for Cartesian products of weakly mixing systems

The generalized purity law for ergodic measures: a simple proof

Sur les supports des transformées de Fourier-Stieltjes

Spectres joints et prolongement des caractères