Topics in ergodic theory and harmonic analysis: an overview

2007 ◽  
pp. 1-8
Author(s):  
Ahmed I. Zayed
Keyword(s):  
Harmonic Analysis ◽  
Ergodic Theory

Odometer actions on G-measures

1991 ◽  
Vol 11 (2) ◽  
pp. 279-307 ◽  
Author(s):  
Gavin Brown ◽  
Anthony H. Dooley
Keyword(s):  
Harmonic Analysis ◽  
Ergodic Theory ◽  
Finite Groups ◽  
Riesz Product ◽  
Direct Sum ◽  
New Methods ◽  
Product Construction ◽  
Ergodic Properties ◽  
Systematic Development

AbstractThe introduction of results from harmonic analysis leads to new methods in the study of the ergodic properties of measures under the action of the direct sum of finite groups. We take the first steps in a systematic development of part of ergodic theory based on the formalism of the Riesz product construction.

Randall Dougherty and Alexander S. Kechris. The complexity of antidifferentiation. Advances in mathematics, vol. 88 (1991), pp. 145–169. - Ferenc Beleznay and Matthew Foreman. The collection of distal flows is not Borel. American journal of mathematics, vol. 117 (1995), pp. 203–239. - Ferenc Beleznay and Matthew Foreman. The complexity of the collection of measure-distal transformations. Ergodic theory and dynamical systems, vol. 16 (1996), pp. 929–962. - Howard Becker. Pointwise limits of subsequences and sets. Fundamenta mathematicae, vol. 128 (1987), pp. 159–170. - Howard Becker, Sylvain Kahane, and Alain Louveau. Some complete sets in harmonic analysis. Transactions of the American Mathematical Society, vol. 339 (1993), pp. 323–336. - Robert Kaufman. PCA sets and convexity Fundamenta mathematicae, vol. 163 (2000), pp. 267–275). - Howard Becker. Descriptive set theoretic phenomena in analysis and topology. Set theory of the continuum, edited by H. Judah, W. Just, and H. Woodin, Mathematical Sciences Research Institute publications, vol. 26, Springer-Verlag, New York, Berlin, Heidelberg, etc., 1992, pp. 1–25.

2001 ◽  
Vol 7 (3) ◽  
pp. 385-388
Author(s):  
Gabriel Debs
Keyword(s):  
New York ◽  
Dynamical Systems ◽  
Harmonic Analysis ◽  
Ergodic Theory ◽  
Set Theory ◽  
American Mathematical Society ◽  
And Topology ◽  
Mathematical Sciences ◽  
Descriptive Set ◽  
The Continuum

scholarly journals Divergence of combinatorial averages and the unboundedness of the trilinear Hilbert transform

2008 ◽  
Vol 28 (5) ◽  
pp. 1453-1464 ◽  
Author(s):  
CIPRIAN DEMETER
Keyword(s):  
Harmonic Analysis ◽  
Ergodic Theory ◽  
Hilbert Transform ◽  
Positive Behavior ◽  
Multilinear Operators ◽  
Similar Range

AbstractWe consider multilinear averages in ergodic theory and harmonic analysis and prove their divergence in some range of Lp spaces. This contrasts with the positive behavior exhibited by these averages in a different range, as proved in Demeter et al [Maximal multilinear operators. Trans. Amer. Math. Soc.360(9) (2008), 4989–5042]. We also prove that the trilinear Hilbert transform is unbounded in a similar range of Lp spaces. The principle underlying these constructions is stated, setting the stage for more general results.

Harmonic Analysis and Ergodic Theory

1941 ◽  
Vol 63 (2) ◽  
pp. 415 ◽  
Author(s):  
Norbert Wiener ◽  
Aurel Wintner
Keyword(s):  
Harmonic Analysis ◽  
Ergodic Theory

Ergodic Theory

1983 ◽  
Author(s):  
Karl E. Petersen
Keyword(s):  
Ergodic Theory
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