Approximate oblique dual frames

In representations using frames, oblique duality appears in situations where the analysis and synthesis has to be done different subspaces. some cases, we cannot obtain an explicit expression for duals others there exists only one dual frame which not properties need. Also, practice computations are exact. To give a solution these problems, this work introduce investigate notion of approximate frames first setting separable Hilbert spaces. We present several provide characterizations frames. focus then on shift-invariant subspaces L^2(R)and g ive conditions generators that assure their existence. The importance from numerical computational point view is illustrated with example sequences generated by B-splines, previous results used construct have better attributes than exact ones. approximation error study its behaviour.