A criterion for the uniform distribution of sequences in compact metric spaces

1987 ◽  
Vol 36 (2) ◽  
pp. 332-342 ◽  
Author(s):  
Robert F. Tichy
Keyword(s):  
Uniform Distribution ◽  
Metric Spaces ◽  
Compact Metric Spaces ◽  
Uniform Distribution Of Sequences

scholarly journals C-uniform distribution on compact metric spaces

1988 ◽  
Vol 129 (1) ◽  
pp. 284-292 ◽  
Author(s):  
Michael Drmota ◽  
Robert F. Tichy
Keyword(s):  
Uniform Distribution ◽  
Metric Spaces ◽  
Compact Metric Spaces

scholarly journals ON BUCK’S UNIFORM DISTRIBUTION IN COMPACT METRIC SPACES

2013 ◽  
Vol 56 (1) ◽  
pp. 61-66
Author(s):  
Milan Paštéka
Keyword(s):  
Uniform Distribution ◽  
Metric Space ◽  
Existence Result ◽  
Metric Spaces ◽  
Theoretic Approach ◽  
Compact Metric Space ◽  
Compact Metric Spaces

ABSTRACT We define uniform distribution in compact metric space with respect to the Buck’s measure density originated in [Buck, R. C.: The measure theoretic approach to density, Amer. J. Math. 68 (1946), 560-580]. Weyl’s criterion is derived. This leads to an existence result.

scholarly journals The Blum-Hanson Property

2019 ◽  
Vol 6 (1) ◽  
pp. 92-105
Author(s):  
Sophie Grivaux
Keyword(s):  
Banach Space ◽  
Hilbert Spaces ◽  
Separable Banach Space ◽  
Metric Spaces ◽  
Compact Metric Spaces ◽  
Theoretic Motivation

AbstractGiven a (real or complex, separable) Banach space, and a contraction T on X, we say that T has the Blum-Hanson property if whenever x, y ∈ X are such that Tnx tends weakly to y in X as n tends to infinity, the means{1 \over N}\sum\limits_{k = 1}^N {{T^{{n_k}}}x} tend to y in norm for every strictly increasing sequence (nk) k≥1 of integers. The space X itself has the Blum-Hanson property if every contraction on X has the Blum-Hanson property. We explain the ergodic-theoretic motivation for the Blum-Hanson property, prove that Hilbert spaces have the Blum-Hanson property, and then present a recent criterion of a geometric flavor, due to Lefèvre-Matheron-Primot, which allows to retrieve essentially all the known examples of spaces with the Blum-Hanson property. Lastly, following Lefèvre-Matheron, we characterize the compact metric spaces K such that the space C(K) has the Blum-Hanson property.

Common fixed points for self mappings on compact metric spaces

2013 ◽  
Vol 219 (12) ◽  
pp. 6804-6808 ◽  
Author(s):  
Cristina Di Bari ◽  
Pasquale Vetro
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Compact Metric Spaces

DIAGONALIZATION MODULO NORM IDEALS AND HAUSDORFF DIMENSIONALITY

2000 ◽  
Vol 11 (08) ◽  
pp. 1057-1078
Author(s):  
JINGBO XIA
Keyword(s):  
Hausdorff Measure ◽  
Metric Spaces ◽  
Adjoint Operator ◽  
Trace Class ◽  
Multiplication Operators ◽  
Von Neumann ◽  
Dimensional Hausdorff Measure ◽  
One Dimensional ◽  
Compact Metric Spaces ◽  
The One

Kuroda's version of the Weyl-von Neumann theorem asserts that, given any norm ideal [Formula: see text] not contained in the trace class [Formula: see text], every self-adjoint operator A admits the decomposition A=D+K, where D is a self-adjoint diagonal operator and [Formula: see text]. We extend this theorem to the setting of multiplication operators on compact metric spaces (X, d). We show that if μ is a regular Borel measure on X which has a σ-finite one-dimensional Hausdorff measure, then the family {Mf:f∈ Lip (X)} of multiplication operators on T2(X, μ) can be simultaneously diagonalized modulo any [Formula: see text]. Because the condition [Formula: see text] in general cannot be dropped (Kato-Rosenblum theorem), this establishes a special relation between [Formula: see text] and the one-dimensional Hausdorff measure. The main result of the paper is that such a relation breaks down in Hausdorff dimensions p>1.

scholarly journals Classification Of Locally 2-Connected Compact Metric Spaces

COMBINATORICA ◽  
2004 ◽  
Vol 25 (1) ◽  
pp. 85-103 ◽  
Author(s):  
Carsten Thomassen
Keyword(s):  
Metric Spaces ◽  
Compact Metric Spaces

scholarly journals AVERAGE SHADOWING PROPERTIES ON COMPACT METRIC SPACES

2006 ◽  
Vol 21 (2) ◽  
pp. 355-361 ◽  
Author(s):  
Jong-Jin Park ◽  
Yong Zhang
Keyword(s):  
Metric Spaces ◽  
Compact Metric Spaces

scholarly journals STOPPED DECISION PROCESS ON COMPACT METRIC SPACES

10.5109/13044 ◽  
1970 ◽  
Vol 14 (1/2) ◽  
pp. 51-60
Author(s):  
Seiichi Iwamoto
Keyword(s):  
Decision Process ◽  
Metric Spaces ◽  
Compact Metric Spaces
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