New spectral multiplicities for ergodic actions

• Autorzy: Anton V. Solomko
• Języki publikacji: EN

Abstrakty

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.

Kategorie tematyczne

• 37A15: General groups of measure-preserving transformations \SeeMainly{}
• 37A30: Ergodic theorems, spectral theory, Markov operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 208
• Numer: 3
• Strony: 229-247

Daty

wydano

2012

Twórcy

autor

Anton V. Solomko

• Institute for Low Temperature Physics & Engineering, National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkov, 61164, Ukraine

Identyfikatory

DOI

10.4064/sm208-3-3