Local Comparability of Measures, Averaging and Maximal Averaging Operators

Averaging and Invariant Measures

An important approach to establishing stochastic behavior of dynamical systems is based on the study of systems expanding a foliation and of measures having smooth densities along the leaves of this foliation [44], [46], [38]. We review recent results on this subject and present some extensions and open questions. 2000 Math. Subj. Class. Primary 34C29; Secondary 37D30.

On Extreme Averaging Operators

Extension and averaging operators for finite fields

In this paper we study L − L estimates of both extension operators and averaging operators associated with the algebraic variety S = {x ∈ Fdq : Q(x) = 0} where Q(x) is a nondegenerate quadratic form over the finite field Fq. In the case when d ≥ 3 is odd and the surface S contains a (d − 1)/2-dimensional subspace, we obtain the exponent r where the L − L extension estimate is sharp. In particul...

Characterization of the ordered weighted averaging operators

This paper deals with the characterization of two classes of monotonic and neutral (MN) aggregation operators . The first class corresponds to (MN) aggregators which are stable for the same positive linear transformations and present the ordered linkage property. The second class deals with (MN)-idempotent aggregators which are stable for positive linear transformations with same unit, independ...

Extended and infinite ordered weighted averaging and sum operators with numerical examples

This study discusses some variants of Ordered WeightedAveraging (OWA) operators and related information aggregation methods. Indetail, we define the Extended Ordered Weighted Sum (EOWS) operator and theExtended Ordered Weighted Averaging (EOWA) operator, which are applied inscientometrics evaluation where the preference is over finitely manyrepresentative works. As...