Quasi-Interpolation Functionals on Spline Spaces Original Research Article

This paper is concerned with the structure of quasi-interpolation functionals on the space spanned by exponential polynomial splines and their translates. The existence of these function is guaranteed by certain conditions which are derived, using the notion of commutators, and shown to be equivalent to some generalization of the Strang-Fix conditions. Characterizations of quasi-interpolation functionals are also formulated, and admissible sets for these functionals are given. Several interpolation schemes are obtained through the quasi-interpolation functionals.