Search results for "30L05"

showing 4 items of 4 documents

SPACES OF SMALL METRIC COTYPE

2010

Naor and Mendel's metric cotype extends the notion of the Rademacher cotype of a Banach space to all metric spaces. Every Banach space has metric cotype at least 2. We show that any metric space that is bi-Lipschitz equivalent to an ultrametric space has infinimal metric cotype 1. We discuss the invariance of metric cotype inequalities under snowflaking mappings and Gromov-Hausdorff limits, and use these facts to establish a partial converse of the main result.

Mathematics::Functional AnalysisPure mathematics30L05 46B85010102 general mathematicsBanach spaceMetric Geometry (math.MG)0102 computer and information sciences16. Peace & justice01 natural sciencesFunctional Analysis (math.FA)Mathematics - Functional AnalysisMetric spaceMathematics - Metric Geometry010201 computation theory & mathematicsConverseMetric (mathematics)FOS: MathematicsMathematics::Metric GeometryGeometry and Topology0101 mathematicsIsoperimetric inequalityUltrametric spaceAnalysisMathematicsJournal of Topology and Analysis
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Isometric embeddings of snowflakes into finite-dimensional Banach spaces

2016

We consider a general notion of snowflake of a metric space by composing the distance by a nontrivial concave function. We prove that a snowflake of a metric space $X$ isometrically embeds into some finite-dimensional normed space if and only if $X$ is finite. In the case of power functions we give a uniform bound on the cardinality of $X$ depending only on the power exponent and the dimension of the vector space.

30L05 46B85 54C25 54E40 28A80Pure mathematicsmetric spacesGeneral MathematicsMathematicsofComputing_GENERALBanach space01 natural sciencesfunctional analysisCardinalityMathematics - Metric GeometryDimension (vector space)0103 physical sciencesFOS: MathematicsMathematics (all)Mathematics::Metric Geometry0101 mathematicsSnowflakeNormed vector spaceMathematicsConcave functionApplied Mathematicsta111010102 general mathematicsnormiavaruudetMetric Geometry (math.MG)normed spacesmetriset avaruudetMetric spacefractalsfraktaalit010307 mathematical physicsfunktionaalianalyysiMathematics (all); Applied MathematicsVector spaceProceedings of the American Mathematical Society
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Dyadic Norm Besov-Type Spaces as Trace Spaces on Regular Trees

2019

In this paper, we study function spaces defined via dyadic energies on the boundaries of regular trees. We show that correct choices of dyadic energies result in Besov-type spaces that are trace spaces of (weighted) first order Sobolev spaces.

Pure mathematicsFunction spacetrace spaceMathematics::Analysis of PDEsMathematics::Classical Analysis and ODEs01 natural sciencesPotential theoryfunktioteoriaregular treeFOS: Mathematicsdyadic norm0101 mathematicsMathematics46E35 30L05Mathematics::Functional Analysis010102 general mathematicsFirst orderFunctional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicsSobolev spaceNorm (mathematics)Besov-type spacepotentiaaliteoriafunktionaalianalyysiAnalysisPotential Analysis
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Geometry and quasisymmetric parametrization of Semmes spaces

2011

We consider decomposition spaces R 3 /G that are manifold factors and admit defining sequences consisting of cubes-with-handles of finite type. Metrics on R 3 /G constructed via modular embeddings of R 3 /G into a Euclidean space promote the controlled topology to a controlled geometry. The quasisymmetric parametrizability of the metric space R 3 /G×R m by R 3+m for any m ≥ 0 imposes quantitative topological constraints, in terms of the circulation and the growth of the cubes-with-handles, on the defining sequences for R 3 /G. We give a necessary condition and a sufficient condition for the existence of such a parametrization. The necessary condition answers negatively a question of Heinone…

decomposition spaceMathematics - Geometric TopologyquasispherequasisymmetryMathematics - Metric GeometryFOS: Mathematics30L10 30L05 30C65parametrizationMetric Geometry (math.MG)Geometric Topology (math.GT)
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