New spectral multiplicities for ergodic actions

Anton V. Solomko. "New spectral multiplicities for ergodic actions." Studia Mathematica 208.3 (2012): 229-247. <http://eudml.org/doc/286144>.

@article{AntonV2012,
abstract = {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.},
author = {Anton V. Solomko},
journal = {Studia Mathematica},
keywords = {spectral multiplicity; ergodic action; (C,F)-construction; Poisson suspension},
language = {eng},
number = {3},
pages = {229-247},
title = {New spectral multiplicities for ergodic actions},
url = {http://eudml.org/doc/286144},
volume = {208},
year = {2012},
}

TY - JOUR
AU - Anton V. Solomko
TI - New spectral multiplicities for ergodic actions
JO - Studia Mathematica
PY - 2012
VL - 208
IS - 3
SP - 229
EP - 247
AB - 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.
LA - eng
KW - spectral multiplicity; ergodic action; (C,F)-construction; Poisson suspension
UR - http://eudml.org/doc/286144
ER -