Extended Chebyshev spaces and weight functions
Résumé
Extended Chebyshev spaces are classical tools in Approximation Theory. More recently they also have been intensively used for geometric design purposes because of the powerful shape parameters they provide. On a given closed bounded interval it is known that a given Extended Chebyshev space can be written as the kernel of a linear differential operator associated with a system of positive weight functions. We determine all systems of weight functions which can be used. This has important applications, e.g., it enables us to build all possible Chebyshevian splines with prescribed section spaces which are "good" for design or interpolation. The result is also closely connected with the construction of Bernstein-Chebyshev operators.