Wyniki wyszukiwania

1

New spectral multiplicities for ergodic actions

100%

Solomko A.

Studia Mathematica

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2012

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tom 208

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nr 3

229-247

EN

Let G be a locally compact second countable Abelian group. Given a measure preserving action T of G on a standard probability space (X,μ), let ℳ (T) denote the set of essential values of the spectral multiplicity function of the Koopman representation $U_{T}$ of G defined in L²(X,μ) ⊖ ℂ by $U_{T}(g)f:= f ∘ T_{-g}$. If G is either a discrete countable Abelian group or ℝⁿ, n ≥ 1, it is shown that the sets of the form {p,q,pq}, {p,q,r,pq,pr,qr,pqr} etc. or any multiplicative (and additive) subsemigroup of ℕ are realizable as ℳ (T) for a weakly mixing G-action T.

2

Infinite measure preserving flows with infinite ergodic index

63%

Danilenko A., Solomko A.

Colloquium Mathematicum

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2009

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tom 115

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nr 1

13-19

EN

We construct a rank-one infinite measure preserving flow $(T_r)_{r∈ ℝ}$ such that for each p > 0, the "diagonal" flow $(T_r × ⋯ × T_r)_{r∈ ℝ} (p times)$ on the product space is ergodic.

3

Simple mixing actions with uncountably many prime factors

63%

Danilenko A., Solomko A.

Colloquium Mathematicum

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2015

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tom 139

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nr 1

37-54

EN

Via the (C,F)-construction we produce a 2-fold simple mixing transformation which has uncountably many non-trivial proper factors and all of them are prime.

Ograniczanie wyników

2 Colloquium Mathematicum

1 Studia Mathematica

3 Solomko A.

2 Danilenko A.

1 2015

1 2012

1 2009

New spectral multiplicities for ergodic actions

Infinite measure preserving flows with infinite ergodic index

Simple mixing actions with uncountably many prime factors