Displaying similar documents to “Multiresolution analysis and Radon measures on a locally compact Abelian group”

Simplicity of Neretin's group of spheromorphisms

Christophe Kapoudjian (1999)

Annales de l'institut Fourier

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Denote by 𝒯 n , n ≥ 2 , the regular tree whose vertices have valence n + 1 , ∂ 𝒯 n its boundary. Yu. A. Neretin has proposed a group N n of transformations of ∂ 𝒯 n , thought of as a combinatorial analogue of the diffeomorphism group of the circle. We show that N n is generated by two groups: the group Aut ( 𝒯 n ) of tree automorphisms, and a Higman-Thompson group G n . We prove the simplicity of N n and of a family of its subgroups.

Pressing Down Lemma for λ -trees and its applications

Hui Li, Liang-Xue Peng (2013)

Czechoslovak Mathematical Journal

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For any ordinal λ of uncountable cofinality, a λ -tree is a tree T of height λ such that | T α | < cf ( λ ) for each α < λ , where T α = { x ∈ T : ht ( x ) = α } . In this note we get a Pressing Down Lemma for λ -trees and discuss some of its applications. We show that if η is an uncountable ordinal and T is a Hausdorff tree of height η such that | T α | ≤ ω for each α < η , then the tree T is collectionwise Hausdorff if and only if for each antichain C ⊂ T and for each limit ordinal α ≤ η with cf ( α ) > ω , { ht ( c ) : c ∈ C } ∩ α is not stationary in α . In the last part of this note, we investigate...

Carleson measures, trees, extrapolation, and T(b) theorems.

Pascal Auscher, Steve Hofmann, Camil Muscalu, Terence Tao, Christoph Thiele (2002)

Publicacions Matemàtiques

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The theory of Carleson measures, stopping time arguments, and atomic decompositions has been well-established in harmonic analysis. More recent is the theory of phase space analysis from the point of view of wave packets on tiles, tree selection algorithms, and tree size estimates. The purpose of this paper is to demonstrate that the two theories are in fact closely related, by taking existing results and reproving them in a unified setting. In particular we give a dyadic version of...