Riesz Sequences of Translates and Generalized Duals with Support on [ 0 , 1 ]
نویسندگان
چکیده
If the integer translates of a function φ 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. We demonstrate that considerable freedom can be obtained by considering oblique duals, i.e., duals not necessarily belonging to W. For example, we present a condition for the existence of oblique duals generated by a function with support on an interval of length one; we further show that the generator can be chosen with desired smoothness. Regardless whether φ is polynomial or not, the same condition implies that a polynomial dual supported on an interval of length one exists.
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