zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Wiener-Wintner return-times ergodic theorem. (English) Zbl 0843.28007
The authors consider ergodic averages of the form 1 Ne inλ f ' (S n y)·f(T n x). They investigate how these averages are related to (and characterize) a new factor of the system (and its orthogonal) – the maximal factor of the type “Abelian group extension of a group rotation” which satisfies a certain functional equation.
MSC:
28D05Measure-preserving transformations
37A99Ergodic theory
References:
[1][A1] I. Assani,A Wiener-Wintner property for the helical transform, Ergodic Theory and Dynamical Systems12 (1992), 185–194.
[2][A2] I. Assani,Uniform Wiener-Wintner theorems for weakly mixing dynamical systems, preprint, unpublished.
[3][B1] J. Bourgain,Return times sequences of dynamical systems, preprint (3/1988), IHES.
[4][B2] J. Bourgain,Double recurrence and almost sure convergence, Journal für die reine und angewandte Mathematik404 (1990), 140–161. · Zbl 0685.28008 · doi:10.1515/crll.1990.404.140
[5][BFKO] J. Bourgain, H. Furstenberg, Y. Katznelson and D. Ornstein,Return times of dynamical systems, Appendix to J. Bourgain’s ”Pointwise Ergodic Theorems For Arithmetic Sets”, Publications IHES69 (1990), 5–45.
[6][CL1] J. P. Conze and E. Lesigne,Théorèmes ergodiques pour des mesures diagonales, Bulletin de la Société Mathématique de France112 (1984), 143–175.
[7][CL2] J. P. Conze and E. Lesigne,Sur un théorème ergodique pour des measures diagonales, Comptes Rendus de l’Academie des Sciences, Paris306, serie I (1988), 491–493.
[8][F] H. Furstenberg,Recurrence in Ergodic Theory and Combinatorial Number Theory, Princeton University Press, Princeton, NJ, 1981.
[9][KN] L. Kuipers and H. Niederreiter,Uniform Distribution of Sequences, J. Wiley and Sons, New York, 1974.
[10][L1] E. Lesigne,Equations fonctionnelles, couplages de produits gauches et théorèmes ergodiques pour measures diagonales, Bulletin de la Société Mathématique de France121 (1993), 315–351.
[11][L2] E. Lesigne,Spectre quasi-discret et théorème ergodique de Wiener-Wintner pour les polynômes, Ergodic Theory and Dynamical Systems, to appear.
[12][R1] D. Rudolph,A joining proof of J. Bourgain’s return times theorem, Ergodic Theory and Dynamical Systems14 (1994), 197–203. · Zbl 0799.28010 · doi:10.1017/S014338570000780X
[13][R2] D. Rudolph,Eigenfunctions of T×S and the Conze-Lesigne algebra, preprint.
[14][WW] N. Wiener and A. Wintner,Harmonic analysis and ergodic theory, American Journal of Mathematics63 (1941), 415–426. · doi:10.2307/2371534