The Experts below are selected from a list of 195 Experts worldwide ranked by ideXlab platform

Remi Boutonnet - One of the best experts on this subject based on the ideXlab platform.

  • Local spectral gap in simple Lie groups and applications
    Inventiones mathematicae, 2017
    Co-Authors: Remi Boutonnet, Adrian Ioana, Alireza Salehi Golsefidy
    Abstract:

    We introduce a novel notion of local spectral gap for general, possibly infinite, Measure preserving actions. We establish local spectral gap for the left translation action $$\Gamma \curvearrowright G$$ Γ ↷ G , whenever $$\Gamma $$ Γ is a dense subgroup generated by algebraic elements of an arbitrary connected simple Lie group G . This extends to the non-compact setting works of Bourgain and Gamburd (Invent Math 171:83–121, 2008 ; J Eur Math Soc (JEMS) 14:1455–1511, 2012 ), and Benoist and de Saxcé (Invent Math 205:337–361, 2016 ). We present several applications to the Banach–Ruziewicz problem, orbit equivalence rigidity, continuous and monotone expanders, and bounded random walks on G . In particular, we prove that, up to a multiplicative constant, the Haar Measure is the unique $$\Gamma $$ Γ -invariant Finitely Additive Measure defined on all bounded measurable subsets of G .

  • Local spectral gap in simple Lie groups and applications
    Inventiones Mathematicae, 2016
    Co-Authors: Remi Boutonnet, Adrian Ioana, Alireza Salehi-golsefidi
    Abstract:

    We introduce a novel notion of local spectral gap for general, possibly infinite, Measure preserving actions. We establish local spectral gap for the left translation action of Γ on G, whenever Γ is a dense subgroup generated by algebraic elements of an arbitrary connected simple Lie group G. This extends to the non-compact setting works of Bourgain and Gamburd [BG06, BG10], and Benoist and de Saxcé [BdS14]. We present several applications to the Banach-Ruziewicz problem, orbit equivalence rigidity, continuous and monotone expanders, and bounded random walks on G. In particular, we prove that, up to a multiplicative constant, the Haar Measure is the unique Γ-invariant Finitely Additive Measure defined on all bounded measurable subsets of G.

  • local spectral gap in simple lie groups and applications
    arXiv: Group Theory, 2015
    Co-Authors: Remi Boutonnet, Adrian Ioana, Alireza Salehi Golsefidy
    Abstract:

    We introduce a novel notion of {\it local spectral gap} for general, possibly infinite, Measure preserving actions. We establish local spectral gap for the left translation action $\Gamma\curvearrowright G$, whenever $\Gamma$ is a dense subgroup generated by algebraic elements of an arbitrary connected simple Lie group $G$. This extends to the non-compact setting recent works of Bourgain and Gamburd \cite{BG06,BG10}, and Benoist and de Saxc\'{e} \cite{BdS14}. We present several applications to the Banach-Ruziewicz problem, orbit equivalence rigidity, continuous and monotone expanders, and bounded random walks on $G$. In particular, we prove that, up to a multiplicative constant, the Haar Measure is the unique $\Gamma$-invariant Finitely Additive Measure defined on all bounded measurable subsets of $G$.

Cho Minhyung - One of the best experts on this subject based on the ideXlab platform.

  • absolute continuity of vitali hahn saks Measure convergence theorems
    International Journal of Theoretical Physics, 2004
    Co-Authors: Wu Junde, Zhou Su, Cho Minhyung
    Abstract:

    In this paper, we prove the following improved Vitali–Hahn–Saks Measure convergence theorem: Let (L, 0, 1) be a Boolean algebra with the sequential completeness property, (G, τ) be an Abelian topological group, ν be a nonnegative Finitely Additive Measure defined on L, {μn: n∈ N} be a sequence of Finitely Additive s-bounded G-valued Measures defined on L, too. If for each a∈ L, {μn(a)}n∈ N is a τ-convergent sequence, for each n∈N, when {ν (aα)}α∈Λ convergent to 0, {μn(aα)}α∈Λ is τ-convergent, then when {ν (aα)}α∈Λ convergent to 0, {μn(aα)}α∈Λ are τ-convergent uniformly with respect to n∈N

  • Absolute Continuity of Vitali–Hahn–Saks Measure Convergence Theorems
    International Journal of Theoretical Physics, 2004
    Co-Authors: Wu Junde, Zhou Su, Cho Minhyung
    Abstract:

    In this paper, we prove the following improved Vitali–Hahn–Saks Measure convergence theorem: Let (L, 0, 1) be a Boolean algebra with the sequential completeness property, (G, τ) be an Abelian topological group, ν be a nonnegative Finitely Additive Measure defined on L, {μn: n∈ N} be a sequence of Finitely Additive s-bounded G-valued Measures defined on L, too. If for each a∈ L, {μn(a)}n∈ N is a τ-convergent sequence, for each n∈N, when {ν (aα)}α∈Λ convergent to 0, {μn(aα)}α∈Λ is τ-convergent, then when {ν (aα)}α∈Λ convergent to 0, {μn(aα)}α∈Λ are τ-convergent uniformly with respect to n∈N

Alireza Salehi Golsefidy - One of the best experts on this subject based on the ideXlab platform.

  • Local spectral gap in simple Lie groups and applications
    Inventiones mathematicae, 2017
    Co-Authors: Remi Boutonnet, Adrian Ioana, Alireza Salehi Golsefidy
    Abstract:

    We introduce a novel notion of local spectral gap for general, possibly infinite, Measure preserving actions. We establish local spectral gap for the left translation action $$\Gamma \curvearrowright G$$ Γ ↷ G , whenever $$\Gamma $$ Γ is a dense subgroup generated by algebraic elements of an arbitrary connected simple Lie group G . This extends to the non-compact setting works of Bourgain and Gamburd (Invent Math 171:83–121, 2008 ; J Eur Math Soc (JEMS) 14:1455–1511, 2012 ), and Benoist and de Saxcé (Invent Math 205:337–361, 2016 ). We present several applications to the Banach–Ruziewicz problem, orbit equivalence rigidity, continuous and monotone expanders, and bounded random walks on G . In particular, we prove that, up to a multiplicative constant, the Haar Measure is the unique $$\Gamma $$ Γ -invariant Finitely Additive Measure defined on all bounded measurable subsets of G .

  • local spectral gap in simple lie groups and applications
    arXiv: Group Theory, 2015
    Co-Authors: Remi Boutonnet, Adrian Ioana, Alireza Salehi Golsefidy
    Abstract:

    We introduce a novel notion of {\it local spectral gap} for general, possibly infinite, Measure preserving actions. We establish local spectral gap for the left translation action $\Gamma\curvearrowright G$, whenever $\Gamma$ is a dense subgroup generated by algebraic elements of an arbitrary connected simple Lie group $G$. This extends to the non-compact setting recent works of Bourgain and Gamburd \cite{BG06,BG10}, and Benoist and de Saxc\'{e} \cite{BdS14}. We present several applications to the Banach-Ruziewicz problem, orbit equivalence rigidity, continuous and monotone expanders, and bounded random walks on $G$. In particular, we prove that, up to a multiplicative constant, the Haar Measure is the unique $\Gamma$-invariant Finitely Additive Measure defined on all bounded measurable subsets of $G$.

Adrian Ioana - One of the best experts on this subject based on the ideXlab platform.

  • Local spectral gap in simple Lie groups and applications
    Inventiones mathematicae, 2017
    Co-Authors: Remi Boutonnet, Adrian Ioana, Alireza Salehi Golsefidy
    Abstract:

    We introduce a novel notion of local spectral gap for general, possibly infinite, Measure preserving actions. We establish local spectral gap for the left translation action $$\Gamma \curvearrowright G$$ Γ ↷ G , whenever $$\Gamma $$ Γ is a dense subgroup generated by algebraic elements of an arbitrary connected simple Lie group G . This extends to the non-compact setting works of Bourgain and Gamburd (Invent Math 171:83–121, 2008 ; J Eur Math Soc (JEMS) 14:1455–1511, 2012 ), and Benoist and de Saxcé (Invent Math 205:337–361, 2016 ). We present several applications to the Banach–Ruziewicz problem, orbit equivalence rigidity, continuous and monotone expanders, and bounded random walks on G . In particular, we prove that, up to a multiplicative constant, the Haar Measure is the unique $$\Gamma $$ Γ -invariant Finitely Additive Measure defined on all bounded measurable subsets of G .

  • Local spectral gap in simple Lie groups and applications
    Inventiones Mathematicae, 2016
    Co-Authors: Remi Boutonnet, Adrian Ioana, Alireza Salehi-golsefidi
    Abstract:

    We introduce a novel notion of local spectral gap for general, possibly infinite, Measure preserving actions. We establish local spectral gap for the left translation action of Γ on G, whenever Γ is a dense subgroup generated by algebraic elements of an arbitrary connected simple Lie group G. This extends to the non-compact setting works of Bourgain and Gamburd [BG06, BG10], and Benoist and de Saxcé [BdS14]. We present several applications to the Banach-Ruziewicz problem, orbit equivalence rigidity, continuous and monotone expanders, and bounded random walks on G. In particular, we prove that, up to a multiplicative constant, the Haar Measure is the unique Γ-invariant Finitely Additive Measure defined on all bounded measurable subsets of G.

  • local spectral gap in simple lie groups and applications
    arXiv: Group Theory, 2015
    Co-Authors: Remi Boutonnet, Adrian Ioana, Alireza Salehi Golsefidy
    Abstract:

    We introduce a novel notion of {\it local spectral gap} for general, possibly infinite, Measure preserving actions. We establish local spectral gap for the left translation action $\Gamma\curvearrowright G$, whenever $\Gamma$ is a dense subgroup generated by algebraic elements of an arbitrary connected simple Lie group $G$. This extends to the non-compact setting recent works of Bourgain and Gamburd \cite{BG06,BG10}, and Benoist and de Saxc\'{e} \cite{BdS14}. We present several applications to the Banach-Ruziewicz problem, orbit equivalence rigidity, continuous and monotone expanders, and bounded random walks on $G$. In particular, we prove that, up to a multiplicative constant, the Haar Measure is the unique $\Gamma$-invariant Finitely Additive Measure defined on all bounded measurable subsets of $G$.

Alireza Salehi-golsefidi - One of the best experts on this subject based on the ideXlab platform.

  • Local spectral gap in simple Lie groups and applications
    Inventiones Mathematicae, 2016
    Co-Authors: Remi Boutonnet, Adrian Ioana, Alireza Salehi-golsefidi
    Abstract:

    We introduce a novel notion of local spectral gap for general, possibly infinite, Measure preserving actions. We establish local spectral gap for the left translation action of Γ on G, whenever Γ is a dense subgroup generated by algebraic elements of an arbitrary connected simple Lie group G. This extends to the non-compact setting works of Bourgain and Gamburd [BG06, BG10], and Benoist and de Saxcé [BdS14]. We present several applications to the Banach-Ruziewicz problem, orbit equivalence rigidity, continuous and monotone expanders, and bounded random walks on G. In particular, we prove that, up to a multiplicative constant, the Haar Measure is the unique Γ-invariant Finitely Additive Measure defined on all bounded measurable subsets of G.