Reproducing fractional monomials: Weakening of the Strang–Fix conditions

Abstract

A method to reproduce causal and symmetric monomials of fractional degree by integer shifts of the corresponding fractional B-splines, introduced by Unser and Blue, is presented. Thus, the traditional relation between the degree of reproduced monomials and the order of approximation holds. Bivariate, obtained by tensor product, fractional B-splines are introduced, and reproducing of bivariate causal and symmetric monomials is shown. Demonstration that the method is based on a weakening of the Strang–Fix conditions is presented.