Norm Convergence of Moving Averages for $\tau$-Integrable Operators

Norm Convergence of Multiple Ergodic Averages for Commuting Transformations

Let T1, . . . , Tl : X → X be commuting measure-preserving transformations on a probability space (X,X , μ). We show that the multiple ergodic averages 1 N PN−1 n=0 f1(T n 1 x) . . . fl(T n l x) are convergent in L2(X,X , μ) as N → ∞ for all f1, . . . , fl ∈ L (X,X , μ); this was previously established for l = 2 by Conze and Lesigne [2] and for general l assuming some additional ergodicity hypo...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

On the Norm Convergence of Nonconventional Ergodic Averages

We offer a proof of the following nonconventional ergodic theorem: Theorem. If Ti : Z y (X,Σ, μ) for i = 1, 2, . . . , d are commuting probability-preserving Z-actions, (IN )N≥1 is a Følner sequence of subsets of Z, (aN )N≥1 is a base-point sequence in Z and f1, f2, . . . , fd ∈ L∞(μ) then the nonconventional ergodic averages

BV-norm convergence of interpolation approximations for Frobenius-Perron operators

Moving Averages

More generally, weighted averages may also be used. Moving averages are also called running means or rolling averages. They are a special case of “filtering”, which is a general process that takes one time series and transforms it into another time series. The term “moving average” is used to describe this procedure because each average is computed by dropping the oldest observation and includi...