Some restriction theorems for the Heisenberg group

S. Thangavelu

Displaying similar documents to “Some restriction theorems for the Heisenberg group”

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

B. Kamiński, Z. Kowalski, P. Liardet (1997)

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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.

Relatively perfect σ-algebras for flows

F. Blanchard, B. Kamiński (1995)

Studia Mathematica

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We show that for every ergodic flow, given any factor σ-algebra ℱ, there exists a σ-algebra which is relatively perfect with respect to ℱ. Using this result and Ornstein's isomorphism theorem for flows, we give a functorial definition of the entropy of flows.

On the directional entropy for ℤ²-actions on a Lebesgue space

B. Kamiński, K. Park (1999)

Studia Mathematica

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We define the concept of directional entropy for arbitrary $ℤ^{2}$ -actions on a Lebesgue space, we examine its basic properties and consider its behaviour in the class of product actions and rigid actions.

An axiomatic definition of the entropy of a $Z^{d}$ -action on a Lebesgue space

B. Kamiński (1990)

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Mixing for dyadic equivalence.

Hasfura-Buenaga, J.R. (1995)

Acta Mathematica Universitatis Comenianae. New Series

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Complete positivity of entropy and non-Bernoullicity for transformation groups

Valentin Golodets, Sergey Sinel'shchikov (2000)

Colloquium Mathematicae

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The existence of non-Bernoullian actions with completely positive entropy is proved for a class of countable amenable groups which includes, in particular, a class of Abelian groups and groups with non-trivial finite subgroups. For this purpose, we apply a reverse version of the Rudolph-Weiss theorem.

Residuality of dynamical morphisms

R. Burton, M. Keane, Jacek Serafin (2000)

Colloquium Mathematicae

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We present a unified approach to the finite generator theorem of Krieger, the homomorphism theorem of Sinai and the isomorphism theorem of Ornstein. We show that in a suitable space of measures those measures which define isomorphisms or respectively homomorphisms form residual subsets.

Slow entropy type invariants and smooth realization of commuting measure-preserving transformations

Anatole Katok, Jean-Paul Thouvenot (1997)

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Spectrum of multidimensional dynamical systems with positive entropy

B. Kamiński, P. Liardet (1994)

Studia Mathematica

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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 $ℤ^{\infty}$ -actions. Next, using its relative version, we extend to $ℤ^{\infty}$ -actions some other general results connecting spectrum and entropy.