Approximate oblique dual frames

Jorge P. Díaz, Sigrid B. Heineken, Patricia M. Morillas

Published 2020-12-21Version 1

In representations using frames, oblique duality appears in situations where the analysis and the synthesis has to be done in different subspaces. In some cases, we cannot obtain an explicit expression for the oblique duals and in others there exists only one oblique dual frame which has not the properties we need. Also, in practice the computations are not exact. To give a solution to these problems, in this work we introduce and investigate the notion of approximate oblique dual frames first in the setting of separable Hilbert spaces. We focus then on approximate oblique dual frames in shift-invariant subspaces of L^2(R). We give different conditions on the generators that assure the existence of approximate oblique dual frames. We present an example that illustrates the results.