共查询到20条相似文献,搜索用时 31 毫秒
1.
Ying Hu 《Journal of Functional Analysis》2008,254(5):1282-1306
We prove maximal ergodic inequalities for a sequence of operators and for their averages in the noncommutative Lp-space. We also obtain the corresponding individual ergodic theorems. Applying these results to actions of a free group on a von Neumann algebra, we get noncommutative analogues of maximal ergodic inequalities and pointwise ergodic theorems of Nevo-Stein. 相似文献
2.
Recently, E.C. Lance extended the pointwise ergodic theorem to actions of the group of integers on von Neumann algebras. Our purpose is to extend other pointwise ergodic theorems to von Neumann algebra context: the Dunford-Schwartz-Zygmund pointwise ergodic theorem, the pointwise ergodic theorem for connected amenable locally compact groups, the Wiener's local ergodic theorem for
+
d
and for general Lie groups. 相似文献
3.
We prove pointwise ergodic theorems for a class of random measures which occurs in Laplacian growth models, most notably in the anisotropic Hastings–Levitov random cluster models. The proofs are based on the theory of quasi-orthogonal functions and uniform Wiener–Wintner theorems. 相似文献
4.
Michael Boshernitzan Grigori Kolesnik Anthony Quas Máté Wierdl 《Journal d'Analyse Mathématique》2005,95(1):63-103
We consider generalizations of the pointwise and mean ergodic theorems to ergodic theorems averaging along different subsequences
of the integers or real numbers. The Birkhoff and Von Neumann ergodic theorems give conclusions about convergence of average
measurements of systems when the measurements are made at integer times. We consider the case when the measurements are made
at timesa(n) or ([a(n)]) where the functiona(x) is taken from a class of functions called a Hardy field, and we also assume that |a(x)| goes to infinity more slowly than some positive power ofx. A special, well-known Hardy field is Hardy’s class of logarithmico-exponential functions.
The main theme of the paper is to point out that for a functiona(x) as described above, a complete characterization of the ergodic averaging behavior of the sequence ([a(n)]) is possible in terms of the distance ofa(x) from (certain) polynomials.
This research was supported by grants from the NSF. 相似文献
5.
Jüri Lember 《Statistics & probability letters》2011,81(2):310-316
We consider the smoothing probabilities of hidden Markov model (HMM). We show that under fairly general conditions for HMM, the exponential forgetting still holds, and the smoothing probabilities can be well approximated with the ones of double-sided HMM. This makes it possible to use ergodic theorems. As an application we consider the pointwise maximum a posteriori segmentation, and show that the corresponding risks converge. 相似文献
6.
Jeremy Avigad 《Annals of Pure and Applied Logic》2009,157(2-3):64-76
The metamathematical tradition, tracing back to Hilbert, employs syntactic modeling to study the methods of contemporary mathematics. A central goal has been, in particular, to explore the extent to which infinitary methods can be understood in computational or otherwise explicit terms. Ergodic theory provides rich opportunities for such analysis. Although the field has its origins in seventeenth century dynamics and nineteenth century statistical mechanics, it employs infinitary, nonconstructive, and structural methods that are characteristically modern. At the same time, computational concerns and recent applications to combinatorics and number theory force us to reconsider the constructive character of the theory and its methods. This paper surveys some recent contributions to the metamathematical study of ergodic theory, focusing on the mean and pointwise ergodic theorems and the Furstenberg structure theorem for measure preserving systems. In particular, I characterize the extent to which these theorems are nonconstructive, and explain how proof-theoretic methods can be used to locate their “constructive content”. 相似文献
7.
V. A. Gorelov 《Mathematical Notes》2013,94(1-2):82-95
We consider hypergeometric functions satisfying homogeneous linear differential equations of arbitrary order. We prove general theorems on the algebraic independence of the solutions of a set of hypergeometric equations as well as of the values of these solutions at algebraic points. The conditions of most theorems are necessary and sufficient. 相似文献
8.
Marco Schreiber 《Semigroup Forum》2013,86(2):321-336
We study mean ergodicity in amenable operator semigroups and establish the connection to the convergence of strong and weak ergodic nets. We then use these results in order to show the convergence of uniform families of ergodic nets that appear in topological Wiener–Wintner theorems. 相似文献
9.
Alexandru D. Ionescu Elias M. Stein Akos Magyar Stephen Wainger 《Acta Mathematica》2007,198(2):231-298
We prove L
p
boundedness of certain non-translation-invariant discrete maximal Radon transforms and discrete singular Radon transforms.
We also prove maximal, pointwise, and L
p
ergodic theorems for certain families of non-commuting operators. 相似文献
10.
We prove pointwise and mean versions of the subadditive ergodic theorem for superstationary families of compact, convex random subsets of a real Banach space, extending previously known results that were obtained in finite dimensions or with additional hypotheses on the random sets. We also show how the techniques can be used to obtain the strong law of large numbers for pairwise independent random sets, as well as results in the weak topology. 相似文献
11.
Anthony To-Ming Lau Koji Nishiura Wataru Takahashi 《Proceedings of the American Mathematical Society》2007,135(10):3143-3150
The purpose of this paper is to show that the study of mean ergodic theorems for almost-orbits of semigroups of nonexpansive mappings on closed convex subsets of a Banach space can be reduced to the study of orbits for semigroups of nonexpansive mappings. This provides a unified approach to various mean ergodic theorems for almost-orbits in the literature and new applications.
12.
We study dynamical properties of automorphisms of compact nilmanifolds and prove that every ergodic automorphism is exponentially mixing and exponentially mixing of higher orders. This allows us to establish probabilistic limit theorems and regularity of solutions of the cohomological equation for such automorphisms. Our method is based on the quantitative equidistribution results for polynomial maps combined with Diophantine estimates. 相似文献
13.
S. G. Dani 《Israel Journal of Mathematics》1982,43(1):62-74
We study the dynamics of projective transformations and apply it to (i) prove that the isotropy subgroups of probability measures
on algebraic homogeneous spaces are algebraic and to (ii) study the class of ergodic quasi-invariant measures of automorphisms
of non-compact Lie groups. It is shown that their support is always a proper subset and that under certain conditions on the
Lie group the induced homeomorphism of the support is topologically equivalent to a translation of a compact group. 相似文献
14.
We summarize seventeen equivalent conditions for the equality of algebraic and geometric multiplicities of an eigenvalue for a complex square matrix. As applications, we give new proofs of some important results related to mean ergodic and positive matrices. 相似文献
15.
We prove two nonlinear ergodic theorems for noncommutative semigroups of nonexpansive mappings in Banach spaces. Using these
results, we obtain some nonlinear ergodic theorems for discrete and one-parameter semigroups of nonexpansive mappings.
Dedicated to Professors Albrecht Dold and Ed Fadell 相似文献
16.
I. Assani 《Journal d'Analyse Mathématique》2010,110(1):241-269
Let (X, B, μ, T) be a measure preserving system. We prove the pointwise convergence of ergodic averages along cubes of 2
k
− 1 bounded and measurable functions for all k. We show that this result can be derived from estimates about bounded sequences of real numbers and apply these estimates
to establish the pointwise convergence of some weighted ergodic averages and ergodic averages along cubes for not necessarily
commuting measure preserving transformations. 相似文献
17.
We present a unified approach to the Darling-Kac theorem and the arcsine laws for occupation times and waiting times for ergodic
transformations preserving an infinite measure. Our method is based on control of the transfer operator up to the first entrance
to a suitable reference set rather than on the full asymptotics of the operator. We illustrate our abstract results by showing
that they easily apply to a significant class of infinite measure preserving interval maps. We also show that some of the
tools introduced here are useful in the setup of pointwise dual ergodic transformations. 相似文献
18.
Estimates for the rate of convergence in ergodic theorems are necessarily spectral. We find the equivalence constants relating
the polynomial rate of convergence in von Neumann’s mean ergodic theorem with continuous time and the polynomial singularity
at the origin of the spectral measure of the function averaged over the corresponding dynamical system. We also estimate the
same rate of convergence with respect to the decrease rate of the correlation function. All results of this article have obvious
exact analogs for the stochastic processes stationary in the wide sense. 相似文献
19.
E.H. el Abdalaoui 《Journal of Mathematical Analysis and Applications》2019,469(2):960-981
It is shown that there is a non-singular dynamical system for which the maximal ergodic inequality does not hold. We further discuss the connection between a non-singular dynamical systems and the pointwise convergence of the Furstenberg ergodic averages. 相似文献
20.
O. Kada 《Proceedings of the American Mathematical Society》1999,127(10):3003-3011
We prove strong mean convergence theorems and the existence of ergodic projection and retraction for commutative semigroups of operators which is Eberlein-weakly almost periodic.