Convergence of polynomial ergodic averages
111 citations recorded by the source corpus.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/496e1908c1b7c91a8b9f8c6af8c3f6174886e31c
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Multiple recurrence and convergence for hardy sequences of polynomial growth (2009, background): “, lp(n)} whenever p is an integer polynomial ([27]).”
- Pointwise ergodic theorems for non-conventional bilinear polynomial averages (2020, background): “The case p1 = · · · = pk =∞, p = 2 is established in [39], [50] (see also [73] for a quite different proof and a generalization); one can then extend to other 0 < p < ∞ by Hölder’s inequality, and the case of general p1, .”
- Ergodic seminorms for commuting transformations and applications (2008, methodology): “2.6. A characteristic σ-algebra on X. The definitions and results of this section are completely similar to those of Section 4.2 of [ HK1 ].”
- Multiple ergodic averages for three polynomials and applications (2006, unknown): “Using methods from [19], this was done in [20] for weak convergence, and in [25] for strong convergence of the averages ( P ).”
- The primes contain arbitrarily long polynomial progressions (2006, methodology): “M1,...,Md!1, choosing the order in which these parameters go to infinity carefully; see [ 21 ].”
- Intersective polynomials and polynomial Szemeredi theorem (2007, background): “It was proved in [L4] (see also [HK2]) that for any probability measure preserving system ( X, T, µ ), a certain pro-nilsystem ( X, T , µ ) is a characteristic factor of ( X, T, µ ) with respect to the system of polynomial actions { T p 1 ( n ) , . . . e e , T p r ( n ) } , which means that ( X, T…”
- Ergodic averages of commuting transformations with distinct degree polynomial iterates (2009, result): “, T are equal, convergence was established after a long series of intermediate results; the papers [11–13, 18, 21, 23, 30, 34] dealt with the important case of linear polynomials, and using the machinery introduced in [23], convergence for arbitrary polynomials was finally obtained in [24] except fo”
- The Green-Tao Theorem on arithmetic progressions in the primes: an ergodic point of view (2005, background): “, fk are known to exist in L 2(μ) (see [22] and [23]).”
- Some open problems on multiple ergodic averages (2011, background): “Kra in [32] except for a few cases that were treated by A.”
- Norm convergence of nilpotent ergodic averages (2011, background): “Here, the case d = 2 was proven by Conze and Lesigne [8] and assuming extra ergodicity hypothesis on the transformations Zhang [21] gave a proof for d = 3 and Frantzikinakis and Kra [9] for general d.”
- Multiple recurrence and convergence for sequences related to the prime numbers (2006, unknown): “(µ) as N → ∞. In [15], it is shown that the limit exists for sn = n (another proof is given in [23]). If q(n) is an integer valued polynomial, the existence of the limit for {q(n): n ∈ N} is shown in [16] (see [17] for a more general result). It was a folklore theorem that for k = 1, the limit exist”