On the convergence of the rotated one-sided ergodic Hilbert transform
نویسندگان
چکیده
Sufficient conditions have been given for the convergence in norm and a.e. of the ergodic Hilbert transform ([11], [5], [6]). Here we apply these conditions to the rotated ergodic Hilbert transform ∑ ∞ n=1 λ n n T f , where λ is a complex number of modulus 1. When T is a contraction in a Hilbert space, we show that the logarithmic Hausdorff dimension of the set of λ’s for which this series does not converge is at most 2 and give examples where this bound is attained.
منابع مشابه
Ergodic Theorems over Sparse Random Subsequences
We prove an L subsequence ergodic theorem for sequences chosen by independent random selector variables, thereby showing the existence of universally L-good sequences nearly as sparse as the set of squares. We extend this theorem to a more general setting of measure-preserving group actions. In addition, we use the same technique to prove an L almost everywhere convergence result for a modulate...
متن کاملOn the Two Dimensional Bilinear Hilbert Transform
We investigate the Bilinear Hilbert Transform in the plane and the pointwise convergence of bilinear averages in Ergodic theory, arising from Z actions. Our techniques combine novel one and a half dimensional phase-space analysis with more standard one dimensional theory.
متن کاملOn the Two Dimensional Bilinear Hilbert Transform Ciprian Demeter and Christoph Thiele
We investigate the Bilinear Hilbert Transform in the plane and the pointwise convergence of bilinear averages in Ergodic theory, arising from Z actions. Our techniques combine novel one and a half dimensional phase-space analysis with more standard one dimensional theory.
متن کاملON THE TWO-DIMENSIONAL BILINEAR HILBERT TRANSFORM By CIPRIAN DEMETER and CHRISTOPH THIELE
We investigate the Bilinear Hilbert Transform in the plane and the pointwise convergence of bilinear averages in Ergodic theory, arising from Z2 actions. Our techniques combine novel one and a half-dimensional phase-space analysis with more standard one-dimensional theory.
متن کاملNon-linear ergodic theorems in complete non-positive curvature metric spaces
Hadamard (or complete $CAT(0)$) spaces are complete, non-positive curvature, metric spaces. Here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. Our results extend the standard non-linear ergodic theorems for non-expansive maps on real Hilbert spaces, to non-expansive maps on Ha...
متن کامل