Norm convergence of nilpotent ergodic averages

By M. N. Walsh. 2011

126 citations recorded by the source corpus.

We show that multiple polynomial ergodic averages arising from nilpotent groups of measure preserving transformations of a probability space always converge in the L^2 norm.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3e3e4eb618800651ee16fedb5fbf8c3fa38fb7b0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. Nikos Frantzikinakis
2. Terence Tao
3. Mariusz Mirek
4. Ben Krause
5. B. Host
6. Van H. Vu
7. Q. Chu
8. T. Ziegler

In Geometry and Topology

1. Nikos Frantzikinakis
2. Terence Tao
3. Mariusz Mirek
4. Ben Krause
5. Q. Chu
6. B. Host
7. Ulrich Kohlenbach
8. M. N. Walsh

In Mathematical Physics

1. Terence Tao
2. Nikos Frantzikinakis
3. Mariusz Mirek
4. Ben Krause
5. Van H. Vu
6. Zihua Guo
7. D. Tataru
8. Carlos E. Kenig

Citations in the corpus

• Some open problems on multiple ergodic averages (2011, methodology): “an convergence of multiple ergodic averages. After a long series of partial results that dealt with commuting transformations [18, 23, 24, 97, 99, 141, 158, 181, 200, 243, 280, 288, 297], M. Walsh in [290] proved the following result: Theorem. Let p1,...,pℓ be integer valued polynomials. Then the av”
• 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, .”