Generalized Chebyshevian Splines

Abstract

In this paper we study a space of splines in which the pieces are drawn from a linear space spanned by an ECT-system U. The splines here generalize the usual Chebyshevian splines in that the pieces in the various intervals are restricted to come from varying subspaces of U. For our class of generalized splines we discuss zeros, determinants associated with certain Lagrange and Hermite interpolation problems, and properties of certain local support basis splines.