Existence and Uniqueness of the Non-Polynomial Spline Spaces with Maximal Smoothness

Abstract: The aims of the paper are to obtain necessary and sufficient conditions of existence and smoothness for non-polynomial spline spaces of order m, to establish the uniqueness of the Bf-spline spaces in the class C m-1 among mentioned spaces (under condition of fixed grid and fixed generating vector function f), and to prove the embedding of the Bf-spline spaces corresponding to embedded grids.