A uniqueness theorem for finitely additive invariant measures on a compact homogeneous space

1981 ◽  
Vol 30 (3) ◽  
pp. 341-344 ◽  
Author(s):  
Rolf Schneider
Keyword(s):  
Homogeneous Space ◽  
Uniqueness Theorem ◽  
Invariant Measures ◽  
Compact Homogeneous Space

A Class of Abstract Linear Representations for Convolution Function Algebras over Homogeneous Spaces of Compact Groups

2018 ◽  
Vol 70 (1) ◽  
pp. 97-116 ◽  
Author(s):  
Arash Ghaani Farashahi
Keyword(s):  
Invariant Measure ◽  
Compact Group ◽  
Homogeneous Space ◽  
Closed Subgroup ◽  
Homogeneous Spaces ◽  
Compact Groups ◽  
Compact Homogeneous Space ◽  
Linear Representations ◽  
Function Algebras ◽  
Convolution Function

AbstractThis paper introduces a class of abstract linear representations on Banach convolution function algebras over homogeneous spaces of compact groups. LetGbe a compact group andHa closed subgroup ofG. Letμbe the normalizedG-invariant measure over the compact homogeneous spaceG/Hassociated with Weil's formula and. We then present a structured class of abstract linear representations of the Banach convolution function algebrasLp(G/H,μ).

On $C^*$-algebras associated to actions of discrete subgroups of $\operatorname{SL}(2,\mathbb{R})$ on the punctured plane

2020 ◽  
Vol 126 (3) ◽  
pp. 540-558
Author(s):  
Jacopo Bassi
Keyword(s):  
Homogeneous Space ◽  
Transformation Group ◽  
Matrix Multiplication ◽  
Crossed Products ◽  
Discrete Subgroups ◽  
Horocycle Flow ◽  
Discrete Transformation ◽  
Compact Homogeneous Space ◽  
C Algebra ◽  
C Algebras

Dynamical conditions that guarantee stability for discrete transformation group $C^*$-algebras are determined. The results are applied to the case of some discrete subgroups of $\operatorname{SL} (2,\mathbb{R} )$ acting on the punctured plane by means of matrix multiplication of vectors. In the case of cocompact subgroups, further properties of such crossed products are deduced from properties of the $C^*$-algebra associated to the horocycle flow on the corresponding compact homogeneous space of $\operatorname{SL} (2,\mathbb{R} )$.

Testing for uniformity on a compact homogeneous space

1968 ◽  
Vol 5 (01) ◽  
pp. 177-195 ◽  
Author(s):  
R. J. Beran
Keyword(s):  
Homogeneous Space ◽  
Invariance Principle ◽  
Compact Homogeneous Space ◽  
Maximal Invariant ◽  
Invariant Test

This paper applies the invariance principle to the problem of testing a distribution on a compact homogeneous space for uniformity. The notion of using a reduction by invariance in such a situation is due to Ajne[1], who considers tests invariant under rotation on a circle. In his paper, he derives the distribution of the maximal invariant and gives the general form of the most powerful invariant test for uniformity on the circle.

Testing for uniformity on a compact homogeneous space

1968 ◽  
Vol 5 (1) ◽  
pp. 177-195 ◽  
Author(s):  
R. J. Beran
Keyword(s):  
Homogeneous Space ◽  
Invariance Principle ◽  
Compact Homogeneous Space ◽  
Maximal Invariant ◽  
Invariant Test

This paper applies the invariance principle to the problem of testing a distribution on a compact homogeneous space for uniformity. The notion of using a reduction by invariance in such a situation is due to Ajne[1], who considers tests invariant under rotation on a circle. In his paper, he derives the distribution of the maximal invariant and gives the general form of the most powerful invariant test for uniformity on the circle.

Epimorphic subgroups and invariant measures

1995 ◽  
Vol 15 (6) ◽  
pp. 1207-1210 ◽  
Author(s):  
Shahar Mozes
Keyword(s):  
Probability Measure ◽  
Homogeneous Space ◽  
Invariant Measures ◽  
Uniquely Ergodic

AbstractIt is shown that a probability measure on a homogeneous space Γ\G which is invariant under a subgroup H < G which is epimorphic in a subgroup L < G is invariant under L. When L = G we obtain a subgroup H such that for any lattice Γ < G its action on Γ\G is uniquely ergodic.

THE SET OF THE INVARIANT MEASURES OF BOUNDED SPIN–FLIP PROCESSES WITH POTENTIAL

1986 ◽  
Vol 6 (2) ◽  
pp. 213-222
Author(s):  
Shouzheng Tang
Keyword(s):  
Invariant Measures ◽  
Spin Flip

Stress state of piece-wise homogeneous space with doubly-periodic system of interphase defects.

2016 ◽  
Vol 69 (3) ◽  
pp. 3-15 ◽  
Author(s):  
. HakobyanV.N ◽  
L.V. Hakobyan
Keyword(s):  
Stress State ◽  
Homogeneous Space ◽  
Periodic System

Teichmuller Geometry

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Uniqueness Theorem ◽  
Existence Theorems ◽  
Quadratic Differentials ◽  
Complex Structures ◽  
Metric Geometry ◽  
Quasiconformal Maps ◽  
Hyperbolic Structures ◽  
Teichmüller Metric ◽  
Uniqueness And Existence ◽  
Teichmüller Mapping

This chapter focuses on the metric geometry of Teichmüller space. It first explains how one can think of Teich(Sɡ) as the space of complex structures on Sɡ. To this end, the chapter defines quasiconformal maps between surfaces and presents a solution to the resulting Teichmüller's extremal problem. It also considers the correspondence between complex structures and hyperbolic structures, along with the Teichmüller mapping, Teichmüller metric, and the proof of Teichmüller's uniqueness and existence theorems. The fundamental connection between Teichmüller's theorems, holomorphic quadratic differentials, and measured foliations is discussed as well. Finally, the chapter describes the Grötzsch's problem, whose solution is tied to the proof of Teichmüller's uniqueness theorem.

Sign in / Sign up

Export Citation Format

Share Document