Riesz sequences of translates and generalized duals with support on [0,1]

Abstract

If the integer translates of a function phi with compact support generate a frame for a subspace W of L-2(R), then it is automatically a Riesz basis for W, and there exists a unique dual Riesz basis belonging to W. Considerable freedom can be obtained by considering oblique duals, i.e., duals not necessarily belonging to W. Extending work by Ben-Artzi and Ron, we characterize the existence of oblique duals generated by a function with support on an interval of length one. If such a generator exists, we show that it can be chosen with desired smoothness. Regardless whether phi is polynomial or not, the same condition implies that a polynomial dual supported on an interval of length one exists.