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Generalized Calderón conditions and regular orbit spaces

Hartmut Führ (2010)

Colloquium Mathematicae

The construction of generalized continuous wavelet transforms on locally compact abelian groups A from quasi-regular representations of a semidirect product group G = A ⋊ H acting on L²(A) requires the existence of a square-integrable function whose Plancherel transform satisfies a Calderón-type resolution of the identity. The question then arises under what conditions such square-integrable functions exist. The existing literature on this subject leaves a gap between sufficient and necessary criteria....

Generalized dimension compression under mappings of exponentially integrable distortion

Aleksandra Zapadinskaya (2011)

Open Mathematics

We prove a dimension compression estimate for homeomorphic mappings of exponentially integrable distortion via a modulus of continuity result by D. Herron and P. Koskela [Mappings of finite distortion: gauge dimension of generalized quasicircles, Illinois J. Math., 2003, 47(4), 1243–1259]. The essential sharpness of our estimate is demonstrated by an example.

Generalized interval exchanges and the 2–3 conjecture

Shmuel Friedland, Benjamin Weiss (2005)

Open Mathematics

We introduce the notion of a generalized interval exchange φ 𝒜 induced by a measurable k-partition 𝒜 = A 1 , . . . , A k of [0,1). φ 𝒜 can be viewed as the corresponding restriction of a nondecreasing function f 𝒜 on ℝ with f 𝒜 ( 0 ) = 0 , f 𝒜 ( k ) = 1 . A is called λ-dense if λ(A i∩(a, b))>0 for each i and any 0≤ a< b≤1. We show that the 2–3 Furstenberg conjecture is invalid if and only if there are 2 and 3 λ-dense partitions A and B of [0,1), such that f 𝒜 ∘ f ℬ = f ℬ ∘ f 𝒜 . We give necessary and sufficient conditions for this equality to hold. We show that...

Generalized iterated function systems, multifunctions and Cantor sets

Maciej Klimek, Marta Kosek (2009)

Annales Polonici Mathematici

Using a construction similar to an iterated function system, but with functions changing at each step of iteration, we provide a natural example of a continuous one-parameter family of holomorphic functions of infinitely many variables. This family is parametrized by the compact space of positive integer sequences of prescribed growth and hence it can also be viewed as a parametric description of a trivial analytic multifunction.

Generalized Lebesgue points for Sobolev functions

Nijjwal Karak (2017)

Czechoslovak Mathematical Journal

In many recent articles, medians have been used as a replacement of integral averages when the function fails to be locally integrable. A point x in a metric measure space ( X , d , μ ) is called a generalized Lebesgue point of a measurable function f if the medians of f over the balls B ( x , r ) converge to f ( x ) when r converges to 0 . We know that almost every point of a measurable, almost everywhere finite function is a generalized Lebesgue point and the same is true for every point of a continuous function. We show...

Generated fuzzy implications and fuzzy preference structures

Vladislav Biba, Dana Hliněná (2012)

Kybernetika

The notion of a construction of a fuzzy preference structures is introduced. The properties of a certain class of generated fuzzy implications are studied. The main topic in this paper is investigation of the construction of the monotone generator triplet ( p , i , j ) , which is the producer of fuzzy preference structures. Some properties of mentioned monotone generator triplet are investigated.

Générateurs indépendants pour les systèmes d'isométries de dimension un

Damien Gaboriau (1997)

Annales de l'institut Fourier

Un système fini d’isométries partielles de R est dit à générateurs indépendants si les composés non triviaux fixent au plus un point. On décrit un procédé simple et naturel pour obtenir des générateurs indépendants, sans modifier les orbites, pour tout système sans composante minimale homogène : en prenant la restriction de chaque générateur à un certain sous-intervalle de son domaine. Un système avec une composante minimale homogène ne possède pas de générateurs indépendants.

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