Search results for "regular tree"

showing 6 items of 6 documents

Trace Operators on Regular Trees

2020

Abstract We consider different notions of boundary traces for functions in Sobolev spaces defined on regular trees and show that the almost everywhere existence of these traces is independent of the chosen definition of a trace.

QA299.6-433Regular treeApplied Mathematics010102 general mathematicsnewtonian space01 natural sciencesAlgebraTrace (semiology)010104 statistics & probabilityregular treetrace operator31e0546e35potentiaaliteoriaGeometry and Topology0101 mathematicsfunktionaalianalyysiAnalysisTrace operatorMathematicsNewtonian space
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2020

Abstract We show that the combination of doubling and (1, p)-Poincaré inequality is equivalent to a version of the Ap-condition on rooted K-ary trees.

Regular treeApplied Mathematics010102 general mathematicsPoincaré inequality01 natural sciencesCombinatoricssymbols.namesake0103 physical sciencessymbols010307 mathematical physicsGeometry and Topology0101 mathematicsAnalysisMathematicsAnalysis and Geometry in Metric Spaces
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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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Trace and density results on regular trees

2019

We give characterizations for the existence of traces for first order Sobolev spaces defined on regular trees.

Trace (linear algebra)Mathematics::Analysis of PDEsBoundary (topology)01 natural sciencesMeasure (mathematics)Potential theorySet (abstract data type)Combinatoricsregular treeMathematics - Metric Geometry0103 physical sciencesEuclidean geometryClassical Analysis and ODEs (math.CA)FOS: Mathematics0101 mathematicsMathematicsdensityMathematics::Functional Analysis010102 general mathematicsMetric Geometry (math.MG)Functional Analysis (math.FA)Sobolev spaceMathematics - Functional AnalysisMathematics - Classical Analysis and ODEs010307 mathematical physicsTree (set theory)46E35 30L99funktionaalianalyysiAnalysisboundary traceNewtonian space
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Classification criteria for regular trees

2021

Esitämme säännöllisten puiden parabolisuudelle yhtäpitäviä ehtoja. We give characterizations for the parabolicity of regular trees. peerReviewed

Regular treeCapacityparabolicitycapacity31C05 31C15 31C45 31E05Mathematics::Analysis of PDEsMetric Geometry (math.MG)ArticlesFunctional Analysis (math.FA)CombinatoricsMathematics - Functional AnalysisfunktioanalyysiMathematics - Analysis of PDEsregular treeHarmonic functionMathematics - Metric Geometryharmonic functionFOS: MathematicsMathematicsAnalysis of PDEs (math.AP)
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Admissibility versus Ap-Conditions on Regular Trees

2020

We show that the combination of doubling and (1, p)-Poincaré inequality is equivalent to a version of the Ap-condition on rooted K-ary trees. peerReviewed

QA299.6-433ap-conditionpoincaré inequalityAp-condition31c45funktioteoria30l99regular treePoincaré inequalitydoubling measure46e35potentiaaliteoriafunktionaalianalyysiAnalysis
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