6533b855fe1ef96bd12afe3e

RESEARCH PRODUCT

Extremal polynomials in stratified groups

Gian Paolo LeonardiDavide VittoneRoberto MontiEnrico Le Donne

subject

Statistics and Probabilityextremal polynomialsMathematics - Differential GeometryPure mathematicsGeodesicStructure (category theory)Group Theory (math.GR)Characterization (mathematics)algebra01 natural sciencesdifferentiaaligeometriaMathematics - Analysis of PDEsMathematics - Metric Geometry53C17FOS: Mathematics0101 mathematicsAlgebraic numberMathematics - Differential Geometry; Mathematics - Differential Geometry; Mathematics - Analysis of PDEs; Mathematics - Group Theory; Mathematics - Metric Geometry; Mathematics - Optimization and Control; 53C17; 49K30; 17B70Mathematics - Optimization and ControlMathematics010102 general mathematicsStatisticsta111polynomitProlongation53C17 49K30 17B70Lie groupMetric Geometry (math.MG)abnormal extremals010101 applied mathematicsNilpotent Lie algebraNilpotentsub-Riemannian geometryabnormal extremals extremal polynomials Carnot groups sub-Riemannian geometryAbnormal extremals; Carnot groups; Extremal polynomials; Sub-Riemannian geometry; Analysis; Statistics and Probability; Geometry and Topology; Statistics Probability and UncertaintyDifferential Geometry (math.DG)Optimization and Control (math.OC)Carnot groups17B70Probability and UncertaintyGeometry and TopologyStatistics Probability and UncertaintyMathematics - Group TheoryAnalysisAnalysis of PDEs (math.AP)Mathematics - Differential Geometry; Mathematics - Differential Geometry; Mathematics - Analysis of PDEs; Mathematics - Group Theory; Mathematics - Metric Geometry; Mathematics - Optimization and Control; 53C17 49K30 17B7049K30

description

We introduce a family of extremal polynomials associated with the prolongation of a stratified nilpotent Lie algebra. These polynomials are related to a new algebraic characterization of abnormal subriemannian geodesics in stratified nilpotent Lie groups. They satisfy a set of remarkable structure relations that are used to integrate the adjoint equations.

yearjournalcountryeditionlanguage
2018-01-01
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