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 dynamical systems. (English) Zbl 1128.37300

Summary: Let (X,,μ,T) be an ergodic dynamical system on the finite measure space (X,,μ). Let 𝒦 denote the Kronecker factor of T, i.e. the closed linear span in L 2 of the eigenfunctions for T. We say that (X,,μ,T) is a Wiener-Wintner (WW) dynamical system of power type α in L 1 if there exists in 𝒦 a dense set of functions f for which the following holds: there exists a finite positive constant C f such that

sup ε |1 N n=1 N fT n e 2πinε | 1 C f N α

for all positive integers N. Examples of ergodic dynamical systems with this WW property include K automorphisms as well as some skew products over irrational rotations. For WW dynamical systems a simpler proof of the almost everywhere double recurrence property, random weights with a break of duality can be obtained. They also provide naturally almost everywhere continuous random Fourier series related to the spectral measure of the transformation.


MSC:
37A05Measure-preserving transformations
28D05Measure-preserving transformations
37A25Ergodicity, mixing, rates of mixing
47A35Ergodic theory of linear operators