Wyniki wyszukiwania

1

Additive functions with respect to expansions over the set of Gaussian integers

100%

Kátai I., Liardet P.

Acta Arithmetica

|

2001

|

tom 99

|

nr 2

173-182

2

Spectrum of multidimensional dynamical systems with positive entropy

100%

Kamiński B., Liardet P.

Studia Mathematica

|

1994

|

tom 108

|

nr 1

77-85

EN

Applying methods of harmonic analysis we give a simple proof of the multidimensional version of the Rokhlin-Sinaǐ theorem which states that a Kolmogorov $ℤ^d$-action on a Lebesgue space has a countable Lebesgue spectrum. At the same time we extend this theorem to $ℤ^∞$-actions. Next, using its relative version, we extend to $ℤ^∞$-actions some other general results connecting spectrum and entropy.

3

On extremal and perfect σ-algebras for $ℤ^{d}$-actions on a Lebesgue space

81%

Kamiński B., Kowalski Z. S., Liardet P.

Studia Mathematica

|

1997

|

tom 124

|

nr 2

173-178

EN

We show that for every positive integer d there exists a $ℤ^d$-action and an extremal σ-algebra of it which is not perfect.

4

On the multiplicity function of ergodic group extensions of rotations

81%

R. Goodson G., Kwiatkowski J., Lemańczyk M., Liardet P.

Studia Mathematica

|

1992

|

tom 102

|

nr 2

157-174

EN

For an arbitrary set A ⊆ ℕ satisfying 1 ∈ A and lcm(m₁,m₂) ∈ A whenever m₁,m₂ ∈ A, an ergodic abelian group extension of a rotation for which the range of the multiplicity function equals A is constructed.

Ograniczanie wyników

3 Studia Mathematica

1 Acta Arithmetica

4 Liardet P.

2 Kamiński B.

1 Kowalski Z. S.

1 Kwiatkowski J.

1 Kátai I.

1 Lemańczyk M.

1 R. Goodson G.

1 2001

1 1997

1 1994

1 1992

Additive functions with respect to expansions over the set of Gaussian integers

Spectrum of multidimensional dynamical systems with positive entropy

On extremal and perfect σ-algebras for $ℤ^{d}$-actions on a Lebesgue space

On the multiplicity function of ergodic group extensions of rotations