On a Bernoulli Property of some Piecewise C2-Diffeomorphisms in ...d.
We show that for a unitary operator U on , where X is a compact manifold of class , , and μ is a finite Borel measure on X, there exists a function that realizes the maximal spectral type of U.
We show the existence of invariant measures for Markov-Feller operators defined on completely regular topological spaces which satisfy the classical positivity condition.
Let Ti (i = 1, 2, ..., d) be commuting null preserving transformations on a finite measure space (X, F, μ) and let 1 ≤ p < ∞. In this paper we prove that for every f ∈ Lp(μ) the averagesAnf(x) = (n + 1)-d Σ0≤ni≤n f(T1n1T2n2 ... Tdnd x)converge a.e. on X if and only if there exists a finite invariant measure ν (under the transformations Ti) absolutely continuous with respect to μ and a sequence {XN} of invariant sets with XN ↑ X such that νB > 0 for all nonnull invariant sets B and...
We describe two methods of obtaining analytic flows on the torus which are disjoint from dynamical systems induced by some classical stationary processes.
Let ũ denote the conjugate Poisson integral of a function . We give conditions on a region Ω so that , the Hilbert transform of f at x, for a.e. x. We also consider more general Calderón-Zygmund singular integrals and give conditions on a set Ω so that is a bounded operator on , 1 < p < ∞, and is weak (1,1).
Let F and G be finitely generated groups of polynomial growth with the degrees of polynomial growth d(F) and d(G) respectively. Let be a continuous action of F on a compact metric space X with a positive topological entropy h(S). Then (i) there are no expansive continuous actions of G on X commuting with S if d(G)