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 M. Unser and Th. 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.