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.
Extremal polynomials in stratified groups / Enrico, Le Donne; Leonardi, Gian Paolo; Roberto, Monti; Davide, Vittone. - In: COMMUNICATIONS IN ANALYSIS AND GEOMETRY. - ISSN 1019-8385. - ELETTRONICO. - 26:4(2018), pp. 723-757. [10.4310/CAG.2018.v26.n4.a3]
Extremal polynomials in stratified groups
LEONARDI, Gian Paolo;
2018
Abstract
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.
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